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Ground states of biharmonic equations with logarithmic weights and critical exponential growth Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-03-05 Imed Abid, Sami Baraket
In this paper, we investigate a fourth-order weighted equation of the form Δ(w(x)|Δu|N2−2Δu)=f(x,u) within the unit ball B of RN. Our focus lies on establishing the existence of solutions under the...
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The dipolar Schramm-Loewner equation for finitely many slits Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-29 Shi-Yi Lan, Jia Zhang
Let Σ be any disjoint union of finitely many simple curves in the strip region. Based on the continuous dependence of dipolar Loewner chains and the pre-compactness of driving functions associated ...
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Existence of solution for a nonlocal elliptic problem with a Robin-type data Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-21 Debajyoti Choudhuri, Rana Alkhal, Kamel Saoudi
The aim of this work is to study the elliptic problem: (−Δp)su+|u|p−2u=μf(x,u)+λu−γ in Ω,u>0 in Ω,Npsu+α(x)|u|p−2u=0 in RN∖Ω, under some conditions on the nonlinearity f. Here 2≤p≤ps∗, μ,λ>0, 0
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Nonexistence and multiplicity results for a fractional weighted (p,q)-Kirchhoff system Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-20 Xiumei Han, Zohreh Naghizadeh, Binlin Zhang
In this article, we study required conditions to guarantee the nonexistence and multiplicity of solutions for a fractional weighted (p,q)-Kirchhoff system by using variational techniques.
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Landau's theorem for harmonic Bloch functions on simply connected domains Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-14 Vasudevarao Allu, Himadri Halder
For α∈(0,∞), let BH,Ω(α) denote the class of harmonic α-Bloch mappings on a proper simply connected domain Ω⊆C. In this article, we study coefficient estimates for harmonic α-Bloch mappings on a pr...
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On universal quotient Blaschke products Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-13 Liulan Li, Tao Qian, Shilin Wang
In this paper, we introduce a new member to the universal families, called universal quotient Blaschke product, which is a formal quotient of two formal infinite Blaschke products. A formal infinit...
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A non-local scalar field problem: existence, multiplicity and asymptotic behavior Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-12 Asma Amira Batahri, Ahmed Attar, Abdelrazek Dieb
The main purpose of this work is to study a non-local scalar field equation in bounded domains. More precisely we consider the semi-linear fractional elliptic problem: (−Δ)su=λup−1−um−1 in Ω,u>0 i...
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Sign-changing solutions for a weighted Kirchhoff problem with exponential growth non-linearity Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-01 Brahim Dridi, Abir Amor Ben Ali, Rached Jaidane
In this work, we establish the existence of solutions that change sign at low energy for a non-local weighted Kirchhoff problem in the set RN,N>2. The non-linearity of the equation is assumed to ha...
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p(x)-biharmonic equations involving Leray–Lions type operators with Hardy potentials Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-06 Jian Liu, Zengqin Zhao
In this article, we investigate p(x)-biharmonic equations involving Leray–Lions type operators with Hardy potentials. New criteria for the existence of at least one or at least three generalized so...
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Improvements to the Montel–Carathéodory theorem for families of Pn-valued holomorphic curves Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-01 Gopal Datt
In this paper, we establish various sufficient conditions for a family of holomorphic mappings on a domain D⊆C into Pn to be normal. Our results are improvements to the Montel–Carathéodory Theorem ...
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Polyanalytic Neumann-n problem in the unit disk Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-26 Heinrich Begehr
An iterated Neumann boundary value problem for the polyanalytic operator is investigated in the unit disc of the complex plane. Although this problem can be treated for domains in the complex plane...
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A critical phenomenon for the least energy solutions to nonlinear scalar field equations Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-22 Jun Wang, Xiaoguang Li
We study the existence of least energy solutions to the nonlinear scalar field equation: (1) −Δu+λu+V(x)u=Q(x)|u|pu,u∈H1(RN), Where V(x),Q(x)∈L∞(RN) are real functions satisfying suitable assump...
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A free boundary problem for discontinuous semilinear elliptic equations in convex ring Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-22 Sabri Bensid
In this paper, we consider the following free boundary problem: (P){Δu=λϕ(x)∑i=1nH(u−μi)inΩ=Ω2∖Ω¯1,u=0on∂Ω2,u=Mon∂Ω1. The domain Ω is a convex ring where Ω1 and Ω2 are bounded convex domains in R...
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Solvability in the sense of sequences for some linear and nonlinear Fredholm operators with the logarithmic Laplacian Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-24 Messoud Efendiev, Vitali Vougalter
We study the solvability of certain linear and nonlinear nonhomogeneous equations in one dimension involving the logarithmic Laplacian and the transport term. In the linear case we show that the co...
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Embedding model and de Branges-Rovnyak spaces in Dirichlet spaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-03 Carlo Bellavita, Eugenio Dellepiane
In this paper we study embeddings between de Branges-Rovnyak spaces H(b) and harmonically weighted Dirichlet spaces D(μ) in terms of the boundary spectrum of b and the support of the measure μ, by ...
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Riemann boundary value problems on the Archimedean spiral Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-28 Shaohua Fan, Hua Liu, ZhiHui Nie
This paper studies the Riemann boundary value problems on the Archimedean spiral. We characterize the functions which are integrable on the Archimedean spiral. We also study the asymptotic behavior...
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Existence of solutions to a critical Kirchhoff equation with logarithmic perturbation Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-28 Qi Li, Yuzhu Han
In this paper, the following Kirchhoff type elliptic equation −(a+b∫Ω|∇u|2dx)Δu=λ|u|q−2uln|u|2+|u|4u, which involves a power type nonlinearity with critical Sobolev exponent and a logarithmic ty...
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On existence and concentration of positive solutions for a fractional Kirchhoff equation with critical exponential growth Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-27 Ruichang Pei, Jihui Zhang
In this paper we consider the following fractional Kirchhoff type problem {(ϵa+ϵb2π∫R2|u(x)−u(y)|2|x−y|2dxdy)(−Δ)12u+V(x)u=f(u)in R,u∈H1/2(R),u>0in R, where ϵ is a positive parameter and a,b>0 ar...
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The Cauchy integral formula for (p, q)-monogenic functions with α-weight in superspace Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-28 Long Gao, Xiaojing Du, Xiaotong Liang, Yonghong Xie
First, some properties for (p,q)-monogenic functions with α-weight in superspace are obtained. Then the Cauchy–Pompeiu formula in superspace is given. Finally, the Cauchy integral formula and the C...
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Weighted composition operators on harmonic Fock spaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-26 Pham Viet Hai
In this paper, we study weighted composition operators on Fock spaces of harmonic functions (briefly as harmonic Fock spaces). The basic properties of such operators (boundedness, compactness, inve...
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Multiple solutions for the logarithmic fractional Kirchhoff equation with critical or supercritical nonlinearity Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-21 Ting Huang, Yan-Ying Shang
In this paper, we study the following logarithmic fractional Kirchhoff equation: (a+b∫R3|(−Δ)s/2u|2dx)(−Δ)su+V(x)u=|u|p−2ulogu2+λ|u|q−2u,inR3, where a, b>0, (−Δ)s is the fractional Laplace opera...
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Eigenoscillations of the Maxwell equation in a domain with oscillating boundary Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-21 Siwar Saidani, Abdessatar Khelifi
We consider the eigenfrequency problem of the magnetic field of Maxwell's equation in a domain Ω of R3 with an inclusion O under perturbation Oδ, which is a thin layer at the wall boundary (skin de...
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On Clifford multivector-valued actions, generalized Dirac equation and quantization of branes Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-21 Carlos Castro Perelman
We explore the construction of a generalized Dirac equation via the introduction of the notion of Clifford multivector-valued actions, which was inspired by the work of Kanatchikov [Kanatchikov IV....
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A Kohn–Nirenberg type domain in Cn Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-14 Junmin Han, Xi Wu, Di Zhao
In this paper, we consider a Kohn–Nirenberg type domain Ω={(z1,…,zn)∈Cn:Rezn+∑j=1n−1(|zj|p+Kj|zj|p−qRezjq+Lj|zj|p−qImzjq)<0} and discuss the existence of supporting surface and peak function at the...
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Mixed local and nonlocal elliptic equation with singular and critical Choquard nonlinearity Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-14 G.C. Anthal, J. Giacomoni, K. Sreenadh
In this article, we study a class of elliptic problems involving both local and nonlocal operators with different orders and a singular nonlinearity in combination with critical Hartree type nonlin...
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Homogenization and corrector result of optimal control problem for Stokes system Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-14 Ritu Raj, Bidhan Chandra Sardar
This article introduces the boundary optimal control problem in an N-dimensional domain governed by the stationary Stokes equations. Controls are applied to the states through Neumann data on the b...
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A generalization of squeezing function Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-03 Abdelwahed Chrih, Youssef Khelifi
In this article, we introduce a new generalized squeezing function defined on bounded domains in Cn and we describe its properties. We compare our generalized squeezing function with the squeezing ...
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Infinitely many solutions for problems involving -Laplacian and -biharmonic operators Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-01 Abdelhakim Sahbani
In this paper, we study by using variational methods, mountain pass theorem, Z2-mountain pass theorem combined with the theory of the generalized Lebesgue Sobolev spaces, the existence and multipli...
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Oversampling on a class of symmetric regular de Branges spaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-30 Luis O. Silva, Julio H. Toloza
A de Branges space B is regular if the constants belong to its space of associated functions and is symmetric if it is isometrically invariant under the map F(z)↦F(−z). Let KB(z,w) be the reproduci...
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Fractional magnetic Schrödinger equations with potential vanishing at infinity and supercritical exponents Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-29 J.C. de Albuquerque, J.L. Santos
This paper focuses on the following class of fractional magnetic Schrödinger equations: (−Δ)Asu+V(x)u=g(|u|2)u+λ|u|q−2u,in RN, where (−Δ)As is the fractional magnetic Laplacian, A:RN→RN is the ma...
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Multiplicity of solutions for a scalar field equation involving a fractional p-Laplacian with general nonlinearity Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-20 H. P. Bueno, O. H. Miyagaki, A. L. Vieira
We prove the existence of infinitely many radially symmetric solutions to the problem (−Δp)su=g(u)inRN,u∈Ws,p(RN), where s∈(0,1), 2≤p<∞, sp≤N, 2≤N∈N and (−Δp)s is the fractional p-Laplacian opera...
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On the total length of Gamma-lines for rational functions Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-14 Yi C. Huang, Jian-Yang Zhang
In this paper, we present a simple direct proof of an integration lemma due to Barsegian, Sergeev and Montes-Rodrigues, and extend to rational functions their upper estimates on the total length of...
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Application of hypergeometric functions to the construction of particular solutions Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-05 B. Y. Irgashev
In this article, by the similarity method, self-similar solutions of higher-order equations with constant and variable coefficients are constructed. Self-similar solutions are expressed in terms of...
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The weighted reproducing kernels of the Reinhardt domain Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-30 Qian Fu, Guantie Deng
In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain containing the origi...
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Nonlinear polyharmonic boundary value problems in the punctured unit ball Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-13 Zeineb Ben Yahia, Zagharide Zine El Abidine
In this paper we investigate the existence and the asymptotic behavior of positive continuous solutions for a class of nonlinear polyharmonic boundary value problems in the punctured unit ball of R...
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On the higher order Kobayashi pseudometric Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-11 Seok Ban, Florian Bertrand, Amir Jaber Chehayeb, Adam Salha, Walid Tabbara
We study the higher order Kobayashi pseudometric introduced by Yu. We first obtain estimates of this pseudometric in a special pseudoconvex domain in C3. We then study the structure of the higher o...
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A class of elliptic problems driven by a mixed local-nonlocal operator Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-13 Zijian Wu, Haibo Chen
In this paper, we consider a class of elliptic problems driven by a mixed local-nonlocal operator. By estimating the critical groups and using Morse theory, the existence of nontrivial solutions is...
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Sharp critical exponents for nonlinear equations with the fractional Laplacian Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-08 Zixia Yuan, Zimin Tang
In this paper we consider two classes of nonlinear partial differential equations with the fractional Laplacian, namely (−Δ)α2(um)=u|u|q−1+w(x),x∈RN,1≤mα and ∂ku∂tk+(−Δ)α2u=uq,(x,t)...
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The Laurent expansion and residue theorem of weighted monogenic functions Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-01 Liping Wang, Liping Luo, Ying Li, Xin Jiang
Firstly, the definition of p order homogeneous weighted right monogenic polynomials is given, and the hypercomplex variables are introduced in order to construct a basis of all homogeneous weighted...
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Some uncertainty principles for the continuous voice transform Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-25 Moussa Faress, Said Fahlaoui
In this paper, after recalling the main properties of the voice transform, we prove its inversion formula, then we present some qualitative uncertainty principles associated with this transform. Fi...
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Existence of solution for the (p, q)-fractional Laplacian equation with nonlocal Choquard reaction and exponential growth Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-28 Nguyen Van Thin, Pham Thi Thuy, Trinh Thi Diep Linh
In this paper, we study the existence of weak solution to (p,q)-fractional Choquard equation in RN as follows Lpsu+Lqsu+V(x)(|u|p−2u+|u|q−2u)=(1|x|μ∗F(u))f(u), where 2≤Ns=p
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Existence of infinitely many solutions for a class of Schrödinger–Poisson equations without any growth and Ambrosetti–Rabinowitz conditions in RN Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-12 Jin-Fu Yang, Jia-Feng Zhang, Wen-Min Li, Qin Qin
In this paper, we study the following kind of Schrödinger–Poisson equations without any growth and Ambrosetti–Rabinowitz conditions: −Δu+V(x)u+(|x|−1∗u2)u−λu=f(u),x∈RN,−Δu+V(x)u+(|x|−1∗u2)u−λu=f(u),x∈RN, where λ<0 , V(x)∈C[0,+∞) is a potential function and satisfies certain conditions. By using variational method, truncation function and Fountain Theorem, we get the existence of infinitely many solutions
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Indefinite Schrödinger equation with nonlinearity sublinear at zero Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-07 Shibo Liu, Chunshan Zhao
We consider stationary Schrödinger equations with indefinite potential and nonlinearity sublinear at u = 0. Using linking theorem and symmetric mountain pass theorem, existence and multiplicity results are obtained.
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Singular elliptic problem with super-quadratic growth in the gradient Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-03 Siham Boukarabila, Ana Primo, Abdelbadie Younes
ABSTRACT In this paper we analyze the existence of solution to the homogeneous Dirichlet for a nonlinear elliptic singular problem, ⎧⎩⎨⎪⎪−Δu=|∇u|q|u|α+λfu=0inΩ,on∂Ω,{−Δu=|∇u|q|u|α+λfinΩ,u=0on∂Ω, where N≥2N≥2 , Ω⊂RNΩ⊂RN is a bounded regular domain, q>2, α0 and f is a nonnegative function belonging to a suitable Lebesgue space. Under additional hypotheses on the data, we are also able to show the uniqueness
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Existence and multiplicity of solutions for m-polyharmonic Kirchhoff problems without Ambrosetti–Rabinowitz conditions Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-30 A. Harrabi, M. K. Hamdani, A. Fiscella
In this paper, we prove the existence of infinitely many solutions for a class of quasilinear elliptic m-polyharmonic Kirchhoff equations where the nonlinear function has a quasicritical growth at infinity and without assuming the Ambrosetti and Rabinowitz type condition. The new aspect consists in employing the notion of a Schauder basis to verify the geometry of the symmetric mountain pass theorem
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Infinitely many nodal solutions for a modified Kirchhoff type equation Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-29 Na Liu, Tao Wang
In this paper, we consider the modified Kirchhoff type equation, that is, the Kirchhoff type equation with a quasilinear term (1) ⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪−(a+b∫R3∣∣∣∇u∣∣∣2dx)Δu+V(∣∣∣∣x∣∣∣∣)u−12Δ(∣∣∣∣u∣∣∣∣2)u=∣∣u∣∣p−2uin R3,u→0as |x|→∞,{−(a+b∫R3|∇u|2dx)Δu+V(|x|)u−12Δ(|u|2)u=|u|p−2uin R3,u→0as |x|→∞, (1) where a, b>0, p∈(4,22∗)p∈(4,22∗) and V(|x|)V(|x|) is a radial potential function and bounded below by a positive
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Frequent hypercyclicity of the tensor products of composition operators on weighted Dirichlet spaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-27 Zhitao Guo
In this paper, we mainly study the frequent hypercyclicity of a scalar multiple of the tensor product of two linear fractional composition operators λCφ⊗CψλCφ⊗Cψ on Sν⊗SνSν⊗Sν , where Sν is the weighted Dirichlet space. We will restrict the discussion to the situations that both φ and ψ are hyperbolic non automorphisms, hyperbolic automorphisms and parabolic automorphisms, respectively. Meanwhile,
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A note on unique continuation of eigenfunctions for p-Laplacian operator in a bounded domain Ω in ℝn with a potential V in Lp(Ω) Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-27 René Erlin Castillo
The aim of this note is to study the problem −div(|∇u|p−2∇u)+V|u|p−2u=0−div(|∇u|p−2∇u)+V|u|p−2u=0 in Ω, where Ω is a bounded domain in RnRn and the potential V is assumed to be not equivalent to zero and lies in Lp(Ω). Also, we establish the strong unique continuation property of the eigenfunctions for the p-Laplacian operator in the case where V∈Lp(Ω).
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Correction Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-24
Published in Complex Variables and Elliptic Equations: An International Journal (Ahead of Print, 2023)
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Complex boundary value problems on a circular triangle Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-23 Hamed Emkanpour, Nasir Taghizadeh
We apply the parqueting-reflection technique for a triangle domain to achieve the points of the complex plane. Then the Cauchy–Schwarz representation formula is construed by the Cauchy–Pompeiu formula and an explicit solution for the Schwarz boundary value problem (BVP) for the non-homogeneous Cauchy–Riemann equation on the triangle is presented. We also discuss the condition of solvability and by
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Order bounded and compact sums of weighted composition-differentiation operators Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-23 Aakriti Sharma, Ajay K. Sharma
In this paper, we characterize bounded, compact, and order bounded sums of weighted composition-differentiation operators from Bergman-type spaces to weighted Banach spaces of analytic functions.
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Improved hardy inequalities on Riemannian manifolds Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-21 Kaushik Mohanta, Jagmohan Tyagi
We study the following version of Hardy-type inequality on a domain Ω in a Riemannian manifold (M,g)(M,g) : ∫Ω|∇u|pgραdVg≥(|p−1+β|p)p∫Ω|u|p|∇ρ|pg|ρ|pραdVg+∫ΩV|u|pραdVg,∀u∈C∞c(Ω).∫Ω|∇u|gpραdVg≥(|p−1+β|p)p∫Ω|u|p|∇ρ|gp|ρ|pραdVg+∫ΩV|u|pραdVg,∀u∈Cc∞(Ω). We provide sufficient conditions on p,α,β,ρp,α,β,ρ and V for which the above inequality holds. This generalizes earlier well-known works on Hardy inequalities
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Conjugacy classification of bicomplex Möbius transformations Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-16 Zekun Li, Binlin Dai
ABSTRACT We investigate the Möbius groups theory in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero-divisors. In this paper, we first generalize classical conjugacy classification to bicomplex analysis. Then we have a discussion of the iterates of a bicomplex Möbius transformation and study the attractive and repulsive fixed points in bicomplex
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Refined Bohr inequality for functions in and in complex Banach spaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-14 Sabir Ahammed, Molla Basir Ahamed
In this paper, we first obtain a refined version of the Bohr inequality of norm-type for holomorphic mappings with lacunary series on the polydisk in CnCn under some restricted conditions. Next, we determine the refined version of the Bohr inequality for holomorphic functions defined on a balanced domain G of a complex Banach space X and take values in the unit disk DD . Furthermore, as a consequence
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Weak-type regularity of the Bergman projection on generalized Hartogs triangles in C3 Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-10 Adam B. Christopherson, Kenneth D. Koenig
For power-generalized Hartogs triangles in C3, the Bergman projection satisfies a weak-type estimate at the upper endpoint of Lp boundedness but not at the lower endpoint. Our work complements related results obtained recently for rational Hartogs triangles in C2 and the punctured unit ball in R3.
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The uniqueness solution for a fractional φ-Laplacian Dirichlet problem and its spectrum Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-07-26 Abderrahmane Lakhdari, Kamel Tahri, Nedra Belhaj Rhouma
In this paper, we demonstrate the existence of a unique weak solution for a nonlocal Kirchhoff problem under Dirichlet boundary conditions, involving the fractional φ-Laplacian operator. Our major outcome is acquired by applying variational approaches and critical points theory. In addition, we analyse the spectrum and the eigenvalues associated to this problem. At the end and under some assumptions
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p-harmonic functions with nonlinear Neumann conditions on the sphere and measure data Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-07-24 Natham Aguirre
We study renormalized solutions to the problem {−Δpu=0|∇u|p−2uν+g(u)=μ in {x∈RN:|x|>1} on {x∈RN:|x|=1}{−Δpu=0 in {x∈RN:|x|>1}|∇u|p−2uν+g(u)=μ on {x∈RN:|x|=1} where 1
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Fractional nonhomogeneous system with Hardy-Littlewood-Sobolev critical nonlinearity Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-07-24 Yanbin Sang, Zhiling Han, Xue Yu
In this paper, we consider the following fractional elliptic system of Choquard type in RNRN ⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪(−Δ)su=(∫RN|v(y)|2∗μ|x−y|μdy)|u|2∗μ−2u+f1(x)(−Δ)sv=(∫RN|u(y)|2∗μ|x−y|μdy)|v|2∗μ−2v+f2(x)u,v∈Ds(RN),inRN,inRN,{(−Δ)su=(∫RN|v(y)|2μ∗|x−y|μdy)|u|2μ∗−2u+f1(x)inRN,(−Δ)sv=(∫RN|u(y)|2μ∗|x−y|μdy)|v|2μ∗−2v+f2(x)inRN,u,v∈Ds(RN), where s∈(0,1)s∈(0,1) , N>2s, 0<μ
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A uniqueness theorem for holomorphic curves on annulus sharing hypersurfaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-07-20 Ha Tran Phuong, Inthavichit Padaphet
Recently, some authors have given the uniqueness theorems for the holomorphic curves on an annulus in hyperplanes in general position and hypersurfaces in general position for Veronese embedding. In this paper, we will give a uniqueness theorem in hypersurfaces in general position.
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Families of homomorphic mappings in the polydisk Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-07-09 Martin Chuaqui, Rodrigo Hernández
We study classes of locally biholomorphic mappings defined in the polydisk PnPn that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations, and show a geometric connection between the order of the classes and a covering property. We show for modified and slightly larger classes that the order