样式： 排序： IF:  GO 导出 标记为已读

Berezin transform and Toeplitz operators on polygonal domains Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210923
Jari TaskinenWe consider reflexive Bergman spaces Ap(Ω) on polygonal domains Ω of the complex plane. With some restrictions to the angles of the boundary of Ω, we show that the boundedness of the Toeplitz operator Tg:Ap(Ω)→Ap(Ω) with a positive symbol g is equivalent to the boundedness of the Berezin transform of g or to g times the area measure being a Carleson measure. The result is also formulated for more general

Optimal Liouville type theorems for porous medium systems with sources Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210922
Dao Trong Quyet, Dao Manh ThangIn this paper, we establish some sharp Liouville type theorems for nonnegative weak supersolutions in RN×R of porous medium equation ut−Δum=up, and of porous medium system {ut−Δum=vpvt−Δvm=uq, where p, q>m>1. More precisely, we show that the sharp conditions for nonexistence of supersolutions to the scalar equation and the system are respectively given by N≤2p−m and N≤max(2(p+1)p(q+1)−m(p+1),2(q+1)q(p+1)−m(q+1))

Least energy signchanging solutions of fractional Kirchhoff–Schrödinger–Poisson system with critical and logarithmic nonlinearity Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210919
Shenghao Feng, Li Wang, Ling HuangIn the present paper, we deal with the following fractional Kirchhoff–Schrödinger–Poisson system with logarithmic and critical nonlinearity: (a+b[u]s2)(−Δ)su+V(x)u+ϕu=λuq−2ulnu2+u2s∗−2u,x∈Ω,(−Δ)tϕ=u2,x∈Ω,u=0,x∈R3∖Ω, where s∈34,1,t∈(0,1),λ,a,b>0,4

selfadjoint product of a composition operator and a maximal differential operator on the Fock space Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210919
Mahmood Haji Shaabani, Mohammad Baseri Nezhad, Pham Viet HaiIn this paper, we are interested in operators arising from the product of a weighted composition operator and a maximal differential operator on the Fock space. Let Tmax and Cu,φ denote a maximal differential operator and a weighted composition operator, respectively. We characterize some Cselfadjoint operators Cu,φTmax with respect to special conjugations C. Moreover, we obtain a partial characterization

The Fekete and Szegö inequality for a class of holomorphic mappings on the unit polydisk in and its application Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210913
Qinghua Xu, Taishun Liu, Jin LuLet C be the familiar class of normalized closetoconvex functions in the unit disk. In Koepf [On the FeketeSzegö problem for closetoconvex functions. Proc Amer Math Soc. 1987;101:89–95], Koepf proved that for a function f(z)=z+∑k=2∞akzk in the class C, a3−λa22≤{3−4λ,λ∈[0,13],13+49λ,λ∈[13,23],1,λ∈[23,1]. As an important application, in the same paper, Koepf showed that a3−a2≤1 for closetoconvex

Quaternionic slice regular functions with some sphere bundles Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210912
J. Oscar GonzálezCervantesIn the hypercomplex analysis, it is well known that the quaternionic slice regular functions are defined on axially symmetric slice domains and that each quaternion is represented in the form x+iy, where x,y∈R and i∈S2 but the mapping ((x,y),i)↦x+iy allows to see that any axially symmetric slice domain is the base space of a trivial sphere bundle. Remember that a sphere bundle is a useful concept in

On bicomplex thirdorder Jacobsthal numbers Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210908
The aim of this work is to consider the bicomplex thirdorder Jacobsthal numbers and to present some properties involving this sequence, including the Binetstyle formulae and the generating functions. Furthermore, Cassini's identity and d'Ocagne's identity for this type of bicomplex numbers are given, and a different way to find the nth term of this sequence is stated using the determinant of a fourdiagonal

Existence of positive solutions to the fractional Kirchhofftype problems involving steep potential well Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210906
The aim of this paper is to study the existence of positive solutions to the fractional Kirchhofftype problems involving steep potential well λV and signchanging nonlinearity f(x)up−2u(2

On the delay differential variational inequalities of parabolic–elliptic type Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210829
In this work, we consider a model of functional differential variational inequalities formulated by a delay differential inclusion and an elliptic variational inequality in Banach spaces. We prove the global solvability of the problem and we have given some sufficient conditions to ensure the existence of decay solutions. Moreover, the existence of a global attractor for the semiflow governed by our

Existence of solution for a supercritical nonlinear Schrödinger equation Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210826
We show existence of solution for a supercritical nonlinear Schrödinger equation on the whole RN by means of an approximation scheme. We prove a Sobolev embedding corresponding to the variable exponent of the equation.

Cyclic behaviour of certain operators on the disc algebra Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210825
We present results concerning the cyclic behaviour of weighted shifts and composition operators on the disc algebra. Most of our proofs use the representations of the dual space of the disc algebra as Banach spaces of analytic functions on the unit disc. Taking into account that no composition operator on the disc algebra can be hypercyclic, the results we obtain show that the composition operators

Compact embeddings for Sobolev spaces of two variable exponents Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210817
We study the compact embedding for Sobolev spaces W01,Φ(G) of two variable exponents, where Φ(x,t)=tp(x)(log(e+t))q(x). Here p(⋅) and q(⋅) are variable exponents satisfying the logHölder and log logHölder conditions, respectively.

Asymptotics of eigenvalues for Toeplitz matrices with rational symbols that have a minimum of the 4th order Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210812
In Barrera M, Grudsky SM. Asymptotics of eigenvalues for pentadiagonal symmetric Toeplitz matrices. In: Large truncated Toeplitz matrices, toeplitz operators, and related topics. Operator theory: advances and applications Vol. 259, Birkhäuser, Cham.; 2017; p. 51–77. we have considered the problem about asymptotic formulas for all eigenvalues of Tn(a), as n goes to infinity, assuming that a is a specific

Riemann problem for bianalytic functions on hsummable curves Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210811
This paper is concerned with the Riemann problem for bianalytic functions on a closed Jordan curve with a certain degree of fractality. We derive a solvability condition under which an explicit solution of this problem is obtained.

Mountain pass solution to a perturbated Hardy–Sobolev equation involving pLaplacian on compact Riemannian manifolds Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210806
ABSTRACT In this paper, we consider the following quasilinear equation: Δp,gu+a(x)up−2u=K(x)up∗(s)−2udg(x,x0)s+h(x)ur−2u,x∈M, where M is a compact Riemannian manifold with dimension n⩾3 without boundary, and x0∈M. Here a(x), K(x) and h(x) are continuous functions on M satisfying some further conditions. The operator Δp,g is the pLaplace–Beltrami operator on M associated with the metric g, and

Positive solutions for a relativistic nonlinear Schrödinger equation with critical exponent and Hardy potential Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210806
ABSTRACT In this paper, using a change of variables and variational method, positive solutions of the stationary relativistic nonlinear Schrödinger equation involving critical exponent and Hardy potential are studied when the potential function has positive lower bound and radial symmetry. We extend the result of Huang, Xiang (Soliton solutions for a quasilinear Schrödinger equation with critical exponent

Homogenization of a boundary optimal control problem governed by Stokes equations Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210804
This article considers an optimal control problem for the stationary Stokes system in a threedimensional domain with a highly oscillating boundary. The controls are acting on the state through the Neumann data on the oscillating part of the boundary with appropriate scaling parameters ϵα with α≥1. The periodic unfolding operators are used to characterize the optimal controls. Using the unfolding operators

On Fredholm solvability and on the index of the generalized Neumann problem for an elliptic equation Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210802
In this paper, we investigate the Fredholm solvability of the generalized Neumann problem for a highorder elliptic equation in the plane. The equivalence of the solvability conditions of the generalized Neumann problem to the complementarity condition (Shapiro–Lopatinsky condition) is proved. The formula for the index of the specified problem in the class C2l,μ(D¯) is calculated.

Runge property and approximation by complete systems of solutions for strongly elliptic equations Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210802
We give an overview of some concepts related to the approximation of solutions of a strongly elliptic operator. A definition of a complete system of classical solutions is given, and we show how using the Runge property, it is possible to extend the completeness of these systems onto strictly internal domains in the L2, H1 and H2 norms. This result is applied to Schrödinger equations with potentials

A lower estimate for weaktype Fourier multipliers Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210801
Asmar et al. [Note on norm convergence in the space of weak type multipliers. J Operator Theory. 1998;39(1):139–149] proved that the space of weaktype Fourier multipliers acting from Lp into Lp,∞ is continuously embedded into L∞. We obtain a sharper result in the setting of abstract Lorentz spaces Λq(X) with 0

Approximation theorems for Pascali systems Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210730
ABSTRACT Based on the Runge theorem for generalized analytic vectors proved by Goldschmidt in 1979, we provide a Mergelyantype and a Carlemantype approximation theorems for solutions of Pascali systems.

Riemann–Hilbert problem on a torus and a vortex patch in a wedge Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210730
An exact formula for the conformal map from the exterior of two slits onto the doubly connected flow domain is obtained when a fluid flows in a wedge about a vortex. The map is employed to determine the potential flow outside the vortex and the vortex domain boundary provided the circulation around the vortex and constant speed on the vortex boundary are prescribed, and there are no stagnation points

Systems of simultaneous differential containments and superordinations in the complex plane Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210728
There are over 100 recent articles in the literature dealing with first, second and thirdorder differential superordinations, containments and inequalities in the complex plane, none of which deals with systems of such topics. This article investigates systems of two secondorder simultaneous differential containments, superordinations and inequalities in two analytic functions p and q defined in

A mean value criterion for plurisubharmonic functions Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210727
In this paper, we prove a criterion for plurisubharmonic functions in terms of integral mean by complex ellipsoids. Moreover, by using the criterion, we prove an analogue of Blaschke–Privalov theorem for plurisubharmonic functions.

An inverse problem for an elliptic equation in a spherical domain Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210726
This paper deals with the problem of determining a radially dependent coefficient a(r) in the equation Δu−a(r)u=0, in the unit sphere Ω from the Dirichlet–Neumann data pair {u,∂u∂ν}∂Ω. We discuss the uniqueness of this determination.

Infinitely many solutions for a doubly nonlocal fractional problem involving two critical nonlinearities Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210722
ABSTRACT In this article, we study the existence of infinitely many nontrivial solutions for the following doubly nonlocal problem involving fractional (p(x),p+)Laplacian. (−Δ)p(x)su+(−Δ)p+su=ur(x)−2u+ups∗(x)−2u+λf(x,u)inΩ,u=0inRN∖Ω. Here, Ω⊂RN is a bounded Lipschitz domain, λ>0, qs∈(0,1),p(⋅,⋅) is a continuous, bounded, symmetric function in RN×RN such that p+=sup(x,y)∈RN×RN{p(x,y)}

Chirality notions and electromagnetic scattering: a mini review Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210722
We review mathematical results on the interaction of timeharmonic electromagnetic waves with ‘geometric’ and ‘electromagnetic’ chiral objects and discuss the relation between these two notions.

Intersection properties for singular radial solutions of quasilinear elliptic equations with Hardy type potentials Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210716
We are interested in singular positive solutions of a quasilinear elliptic equation with a singular coefficient r−(γ−1)(rαu′β−1u′)′+krα−β−γuβ+up=0,0β, 0

Monotonicity of solutions for a class of uniformly elliptic nonlocal Bellman systems Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210714
This paper is concerned with a class of uniformly elliptic nonlocal Bellman systems in unbounded Lipschitz domains. There are two major ingredients. The first is a narrow region principle in unbounded domains. We can use this to carry out the direct method of moving planes. The second ingredient is to prove the monotonicity of positive bounded solutions for a cooperative system with uniformly elliptic

Fractional KleinGordon equation with singular mass. II: hypoelliptic case Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210714
In this paper we consider a fractional wave equation for hypoelliptic operators with a singular mass term depending on the spacial variable and prove that it has a very weak solution. Such analysis can be conveniently realised in the setting of graded Lie groups. The uniqueness of the very weak solution, and the consistency with the classical solution are also proved, under suitable considerations

Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210708
A. R. Akhmatova, E. S. Aksenova, V. A. Sloushch, T. A. SuslinaIn L2(R), consider a secondorder elliptic differential operator Aϵ, ϵ>0, of the form Aϵ=−ddxg(x/ϵ)ddx+ϵ−2p(x/ϵ) with periodic coefficients. For small ε, we study the behavior of the semigroup e−Aϵt, t>0, cut by the spectral projection of the operator Aϵ for the interval [ϵ−2ν,+∞). Here ϵ−2ν is the right edge of a spectral gap for the operator Aϵ. We obtain approximation for the ‘cut semigroup’ in

Radial ground state solutions for Choquard equations with HardyLittlewoodSobolev lower critical growth Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210706
YongYong Li, GuiDong Li, ChunLei TangIn this paper, we investigate the following autonomous Choquard equation −Δu+u=(Iα∗F(u))F′(u)in RN, where N≥3, Iα denotes the Riesz potential of order α∈(0,N) and F satisfies general critical growth conditions. By using the variational methods and the Pohožaev manifold techniques, we prove the existence of radially symmetric positive ground state solution.

Gmonogenic mappings in a threedimensional noncommutative algebra Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210706
Tetiana Kuzmenko, Vitalii ShpakivskyiIn this paper, we consider some threedimensional noncommutative algebra A~2 over the field C, which contains the algebra of bicomplex numbers B(C) as a subalgebra. Locally bounded and Gâteauxdifferentiable mappings defined in the domains of the threedimensional subspace of the algebra B(C) and taking values in the algebra A~2 are considered. Such mappings generalize holomorphic functions of bicomplex

On a class of degenerate quasilinear elliptic equations with zero mass Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210706
José Francisco de Oliveira, Olímpio H. Miyagaki, Sandra I. MoreiraExistence of radially symmetric positive solutions for a general class of quasi linear elliptic equations in the zero mass situation is proven. Our results include groundstate solutions for both powertype and exponentialtype critical growths in the whole space and the class concerned includes, as particular cases, the Laplace, pLaplace and kHessian operators in radial form.

On algebraic differential equations concerning the Riemannzeta function and the Eulergamma function Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210706
Qiongyan Wang, Zhi Li, Manli Liu, Nan LiIn this paper, we prove that ζ is not a solution of any nontrivial algebraic differential equation whose coefficients are polynomials in Γ(α),Γ(n),Γ(l) over the ring of polynomials in C, l>n>α≥0 are nonnegative integers. We extend the result that ζ does not satisfy any nontrivial algebraic differential equation whose coefficients are polynomials in Γ,Γ′,Γ″ over the field of complex numbers, which

On mixed norm holomorphic grand and small spaces Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210706
Alexey KarapetyantsIn this paper, we continue the study of new weighted spaces of holomorphic functions on the unit disc with the mixed norm defined in terms of conditions on Fourier coefficients of a function. Here we present the case in which the corresponding conditions are related to grand and small Lebesgues spaces, i.e. the Fourier coefficients as functions of radial variable belong to either grand or small space

On C*algebras of singular integral operators with PQC coefficients and shifts with fixed points Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210706
M. Amélia Bastos, Cláudio A. Fernandes, Yuri I. KarlovichA Fredholm representation on a Hilbert space, whose kernel coincides with the ideal of compact operators, is constructed for the C∗algebra B generated by all multiplication operators by piecewise quasicontinuous (PQC) functions, by the Cauchy singular integral operator ST and by the unitary weighted shift operators Ug:φ↦g′1/2(φ∘g), g∈G, acting on the space L2(T) over the unit circle T⊂C. Here G

On signchanging solutions for quasilinear SchrödingerPoisson system with critical growth Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210706
Jing Zhang, Sihua LiangIn this paper, we consider the following quasilinear SchrödingerPoisson system with critical growth: −Δu+V(x)u−12uΔ(u2)+ϕu=u4u+μg(u),x∈R3,−Δϕ=u2,x∈R3, where μ>0, V(x) is a smooth potential function and g is a appropriate nonlinear function. For the sake of overcoming the technical difficulties caused by the quasilinear term, we shall apply the perturbation method by adding a 4Laplacian operator

Signchanging solutions for modified Schrödinger–Poisson system with general nonlinearity Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210701
Xueqin Peng, Gao Jia, Chen HuangThis paper is concerned with the existence and multiplicity of signchanging solutions for the following modified Schrödinger–Poisson system: −Δu+V(x)u+κϕu−12u△u2=f(u),x∈R3,−△ϕ=u2,x∈R3, where κ∈(0,1),V(x) is coercive, the nonlinear term f is 4superlinear at infinity but does not need any increasing condition. By using the method of invariant sets of descending flow, the existence and multiplicity

Liouvilletype theorems for a system of fractional Laplacian equations Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210701
Rong Yin, Jihui Zhang, Xudong ShangIn the paper, we study the following system of partial differential equations (PDEs) involving fractional Laplacian operators (1) (−△)α2u=vq,x∈R+n,(−△)β2v=up,x∈R+n,(1) under the boundary conditions u≡0, v≡0, x∈Rn∖R+n, where p∈(1,n+βn−α], q∈(1,n+αn−β], 0<α, β<2 and n≥3. In order to overcome the difficulty that there are no corresponding maximum principles for the operators (−△)α2 and (−△)β2 in R+n,

Positive solution to singular semilinear elliptic problems Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210701
Dharmendra KumarIn this paper, we study the existence and regularity of a nontrivial weak solution to the following semilinear elliptic problem with singular weights and singular nonlinearity: {−div(x−2β∇w)−μwx2(β+1)=g(x)wθ1+f(x)wθ2inΩ,w>0inΩ,w=0on∂Ω, under assumptions θ1≥θ2>0,0<μ<(N−2(β+1)2)2 and 0≤g∈Lk(Ω), 0≤f∈Lk(Ω),1

Surjectivity of the ̄∂operator between weighted spaces of smooth vectorvalued functions Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210630
K. KruseWe derive sufficient conditions for the surjectivity of the Cauchy–Riemann operator ∂¯ between weighted spaces of smooth Fréchetvalued functions. This is done by establishing an analog of Hörmander's theorem on the solvability of the inhomogeneous Cauchy–Riemann equation in a space of smooth Cvalued functions whose topology is given by a whole family of weights. Our proof relies on a weakened variant

Maximal ideals in a bicomplex algebra and bicomplex Gelfand–Mazur theorem Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210630
Romesh Kumar, Kulbir SinghIn this paper, we study the maximal ideals in a commutative ring of bicomplex numbers and then we describe the maximal ideals in a bicomplex algebra. We found that the kernel of a nonzero multiplicative BClinear functional in a commutative bicomplex Banach algebra need not be a maximal ideal. Finally, we introduce the notion of bicomplex division algebra and generalize the Gelfand–Mazur theorem for

Meromorphic solutions of one certain type of nonlinear complex differential equation Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210624
Jie Zhang, Liangwen LiaoIn this paper, we are mainly concerned with one certain type of nonlinear complex differential equation fn(z)+Pd(z,f)=p1eα1z+p2eα2z, where p1,p2,α1,α2 are nonzero constants and Pd(z,f) is a differential polynomial in f of degree d at most n−1. For this kind of equation, if it admits a meromorphic solution such that N(r,f)=S(r,f), then firstly we give a positive answer to Li's question with a weaker

Publisher's note Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210623
(2021). Publisher's note. Complex Variables and Elliptic Equations: Vol. 66, Boundary Value Problems for Partial Differential Equations and Function Spaces  Special Issue Dedicated to the 110th Anniversary of the Birthday of Sergei L. Sobolev. Guest Editors: Heinrich Begehr, Gennadii V. Demidenko, and Inessa I. Matveeva, pp. 12091210.

Correction Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210623
(2021). Correction. Complex Variables and Elliptic Equations: Vol. 66, Boundary Value Problems for Partial Differential Equations and Function Spaces  Special Issue Dedicated to the 110th Anniversary of the Birthday of Sergei L. Sobolev. Guest Editors: Heinrich Begehr, Gennadii V. Demidenko, and Inessa I. Matveeva, pp. 12111211.

Correction Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210623
(2021). Correction. Complex Variables and Elliptic Equations: Vol. 66, Boundary Value Problems for Partial Differential Equations and Function Spaces  Special Issue Dedicated to the 110th Anniversary of the Birthday of Sergei L. Sobolev. Guest Editors: Heinrich Begehr, Gennadii V. Demidenko, and Inessa I. Matveeva, pp. 12121212.

Positive solutions to superlinear semipositone problems on the exterior of a ball Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210616
Anumol Joseph, Lakshmi SankarWe consider the problem {−Δu=λK(x)f(u)in B1c,u(x)=0on ∂B1,u(x)→0as x→∞, where B1c={x∈Rn:x>1}, n>2, λ is a positive parameter, K:B1c→R+ belongs to a class of continuous functions which satisfy certain decay assumptions, and f:[0,∞)→R belongs to a class of continuous functions which are superlinear at ∞ with f(0)<0. Recently, several authors have studied positive radial solutions to this problem

Two remarks on the Poincaré metric on a singular Riemann surface foliation Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210609
Sahil Gehlawat, Kaushal VermaLet F be a smooth Riemann surface foliation on M∖E, where M is a complex manifold and E⊂M is a closed set. Fix a hermitian metric g on M∖E and assume that all leaves of F are hyperbolic. For each leaf L⊂F, the ratio of gL, the restriction of g to L, and the Poincaré metric λL on L defines a positive function η that is known to be continuous on M∖E under suitable conditions on M, E. For a domain U⊂M

The second Hankel determinant for starlike and convex functions of order alpha Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210604
Young Jae Sim, Derek K. Thomas, Paweł ZaprawaIn recent years, the study of Hankel determinants for various subclasses of normalised univalent functions f∈S given by f(z)=z+∑n=2∞anzn for D={z∈C:z<1} has produced many interesting results. The main focus of interest has been estimating the second Hankel determinant of the form H2,2(f)=a2a4−a32. A nonsharp bound for H2,2(f) when f∈K(α), α∈[0,1) consisting of convex functions of order α was found

Schwarz boundary value problem on Reuleaux triangle Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210602
Yanshuai Hao, Liu HuaWe discuss the Schwarz problem on Reuleaux triangle. By the technique of parqueting reflection principle, we translate the Schwarz problem into a Riemann boundary value problem on a system of arcs. We first state that the Riemann problem is solvable, while the solutions are represented by a Cauchy type integral. At last, as the main theorem, we prove that those two problems are equivalent to each other

Complex linear differential equations with solutions in the H2K spaces Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210602
Yu Sun, Jinlin Liu, Guangming HuIn this paper, we give the nth derivertive criterion for functions belonging to function spaces HK2. Furthermore, some sufficient conditions for coefficients of the linear differential equation f(k)+Ak−1(z)f(k−1)+⋯+A1(z)f′+A0(z)f=Ak(z)are found such that all solutions belong to the HK2 spaces, where Aj(z) are analytic functions in D, j=0,…,k.

Composition operator between normal weight Dirichlet type space and Bloch type space Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210602
Xuejun Zhang, Ying HuangLet μ be a normal function on [0,1) and p>0. Suppose φ is a holomorphic selfmap on the unit ball B of Cn. In this paper, the authors characterize the conditions such that the composition operator Cφ is bounded or compact from the normal weight Dirichlet type space Dμp(B) to the normal weight Bloch type space Bνp(B) when n>1, where νp(r)=(1−r2)npμ1p(r) ( 0≤r<1). Moreover, the authors give a simple

Multiple solutions for a quasilinear Schrödinger equation involving critical Hardy–Sobolev exponent with Robin boundary condition Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210602
Yin Deng, Gao JiaIn this paper, we consider the existence of multiple solutions for a quasilinear Schrödinger equation with Robin boundary condition involving critical Hardy–Sobolev exponent as follows: −Δu−Δ(u2)u+u=(u2)2∗(s)−1xsu+f(x,u)inΩ,∂u∂n+β(x)u=0on∂Ω, where f∈C(Ω¯×R,R) satisfies suitable condition. Using variable substitution and Mountain Pass Theorem, we prove that the above equation admits at least two nontrivial

Finite zerobased invariant subspaces of the shift operator on reproducing kernel spaces Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210602
Caixing Gu, Jaehui ParkWe characterize wandering subspace property of the shift operator on zerobased invariant subspaces of reproducing kernel Hilbert spaces by using the kernels of Toeplitz operators. As applications, we prove that the wandering subspace property of the shift operator holds on the weighted Bergman space Aα2 ( α>1) for zerobased invariant subspaces when the zeros lie in a small disk centred at the origin

Pohozaevtype identities for a pseudorelativistic Schrödinger operator and applications Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210602
H. Bueno, Aldo H. S. Medeiros, G. A. PereiraWe prove a Pohozaevtype identity for both the problem (−Δ+m2)su=f(u) in RN and its harmonic extension to R+N+1 when 0

Invariance and existence analysis of viscoelastic equations with nonlinear damping and source terms on corner singularity Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210531
Morteza Koozehgar KallejiThe present article is concerned with a class of cornerdegenerate viscoelastic higher hyperbolic equations with nonlinear damping and boundary source terms. First, we prove some invariance results about the energy functional and the solution set of our problem by using potential wells methods on the manifolds with corner singularity. Then, we establish existence results of global weak solution on

Extension of CR structures on pseudoconvex CRmanifolds with comparable eigenvalues of the Leviform Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210527
Sanghyun ChoLet M¯ be a smoothly bounded orientable pseudoconvex CR manifold of finite 1type with comparable eigenvalues of the Leviform. Then we extend the given CR structure on M¯ to an integrable almost complex structure on the concave side of M when dimRM≥3. If dimRM≥7, we extend the structure on the convex side. Therefore we may regard M as a real hypersurface in Cn when dimRM≥7.

Patterns with prescribed numbers of critical points on topological tori Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210527
Putri Zahra Kamalia, Shigeru SakaguchiWe study the existence of critical points of stable stationary solutions to reaction–diffusion problems on topological tori. Stable nonconstant stationary solutions are often called patterns. We construct topological tori and patterns with prescribed numbers of critical points whose locations are explicit.

Existence and multiplicity of solutions for generalized quasilinear Schrödinger equations Complex Var. Elliptic Equ. (IF 0.846) Pub Date : 20210526
XueLin Gui, Bin GeWe consider the generalized quasilinear Schrödinger equations (P) −div(g2(u)∇u)+g(u)g′(u)∇u2+V(x)u=λf(x,u),x∈RN,(P) where N≥3, g:R→R+ is an even differentiable function, f:RN×R→R satisfies the Carathéodory condition, the potential V(x):RN→(0,∞) is continuous and λ is a parameter. The intention of the article is to determine the precise positive interval of λ when the problem possesses at least two