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Convergence analysis for double phase obstacle problems with multivalued convection term Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-11-26 Shengda Zeng; Yunru Bai; Leszek Gasiński; Patrick Winkert
In the present paper, we introduce a family of the approximating problems corresponding to an elliptic obstacle problem with a double phase phenomena and a multivalued reaction convection term. Denoting by 𝓢 the solution set of the obstacle problem and by 𝓢n the solution sets of approximating problems, we prove the following convergence relation
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Fixed point of some Markov operator of Frobenius-Perron type generated by a random family of point-transformations in ℝd Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2021-01-16 Peter Bugiel; Stanisław Wędrychowicz; Beata Rzepka
Existence of fixed point of a Frobenius-Perron type operator P : L1 ⟶ L1 generated by a family {φy}y∈Y of nonsingular Markov maps defined on a σ-finite measure space (I, Σ, m) is studied. Two fairly general conditions are established and it is proved that they imply for any g ∈ G = {f ∈ L1 : f ≥ 0, and ∥f∥ = 1}, the convergence (in the norm of L1) of the sequence {Pjg}j=1∞ to a unique fixed point g0
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Blowing-up solutions of the time-fractional dispersive equations Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2021-01-12 Ahmed Alsaedi; Bashir Ahmad; Mokhtar Kirane; Berikbol T. Torebek
This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented
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Analysis of a diffusive host-pathogen model with standard incidence and distinct dispersal rates Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-12-31 Jinliang Wang; Renhao Cui
This paper concerns with detailed analysis of a reaction-diffusion host-pathogen model with space-dependent parameters in a bounded domain. By considering the fact the mobility of host individuals playing a crucial role in disease transmission, we formulate the model by a system of degenerate reaction-diffusion equations, where host individuals disperse at distinct rates and the mobility of pathogen
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Local versus nonlocal elliptic equations: short-long range field interactions Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-12-31 Daniele Cassani; Luca Vilasi; Youjun Wang
In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter
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Periodic solutions for a differential inclusion problem involving the p(t)-Laplacian Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-12-19 Peng Chen; Xianhua Tang
In the present paper, we consider the nonlinear periodic systems involving variable exponent driven by p(t)-Laplacian with a locally Lipschitz nonlinearity. Our arguments combine the variational principle for locally Lipschitz functions with the properties of the generalized Lebesgue-Sobolev space. Applying the non-smooth critical point theory, we establish some new existence results.
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An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-12-20 Ángel D. Martínez; Daniel Spector
It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate. While these inequalities are optimal for general functions of bounded mean oscillation, the main result of this paper is an improvement for functions in a class
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Regularity for commutators of the local multilinear fractional maximal operators Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-12-08 Xiao Zhang; Feng Liu
In this paper we introduce and study the commutators of the local multilinear fractional maximal operators and a vector-valued function b⃗ = (b1, …, bm). Under the condition that each bi belongs to the first order Sobolev spaces, the bounds for the above commutators are established on the first order Sobolev spaces.
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The concentration-compactness principles for Ws,p(·,·)(ℝN) and application Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-12-08 Ky Ho; Yun-Ho Kim
We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.
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Combined effects of Choquard and singular nonlinearities in fractional Kirchhoff problems Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-12-03 Fuliang Wang; Die Hu; Mingqi Xiang
The aim of this paper is to study the existence and multiplicity of solutions for a class of fractional Kirchho problems involving Choquard type nonlinearity and singular nonlinearity. Under suitable assumptions, two nonnegative and nontrivial solutions are obtained by using the Nehari manifold approach combined with the Hardy-Littlehood-Sobolev inequality.
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Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-12-01 Zhipeng Yang; Fukun Zhao
In this paper, we study the singularly perturbed fractional Choquard equation
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Global solvability in a three-dimensional Keller-Segel-Stokes system involving arbitrary superlinear logistic degradation Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-12-01 Yulan Wang; Michael Winkler; Zhaoyin Xiang
The Keller-Segel-Stokes system
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Concentration results for a magnetic Schrödinger-Poisson system with critical growth Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-11-27 Jingjing Liu; Chao Ji
This paper is concerned with the following nonlinear magnetic Schrödinger-Poisson type equation
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Boundary value problems associated with singular strongly nonlinear equations with functional terms Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-11-12 Stefano Biagi; Alessandro Calamai; Cristina Marcelli; Francesca Papalini
We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type
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Multiple solutions for weighted Kirchhoff equations involving critical Hardy-Sobolev exponent Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-11-07 Zupei Shen; Jianshe Yu
In this article, we consider a class of Kirchhoff equations with critical Hardy-Sobolev exponent and indefinite nonlinearity, which has not been studied in the literature. We prove very nicely that this equation has at least two solutions in ℝ3. And some known results in the literature are improved.
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Existence, multiplicity and nonexistence results for Kirchhoff type equations Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-10-30 Wei He; Dongdong Qin; Qingfang Wu
In this paper, we study following Kirchhoff type equation:
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On a degenerate hyperbolic problem for the 3-D steady full Euler equations with axial-symmetry Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-10-18 Yanbo Hu; Fengyan Li
The transonic channel flow problem is one of the most important problems in mathematical fluid dynamics. The structure of solutions near the sonic curve is a key part of the whole transonic flow problem. This paper constructs a local classical hyperbolic solution for the 3-D axisymmetric steady compressible full Euler equations with boundary data given on the degenerate hyperbolic curve. By introducing
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Exponential stability of the nonlinear Schrödinger equation with locally distributed damping on compact Riemannian manifold Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-10-18 Fengyan Yang; Zhen-Hu Ning; Liangbiao Chen
In this paper, we consider the following nonlinear Schrödinger equation:
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On a class of critical elliptic systems in ℝ4 Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-09-13 Xin Zhao; Wenming Zou
In the present paper, we consider the following classes of elliptic systems with Sobolev critical growth:
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Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-09-02 Michal Bathory; Miroslav Bulíček; Josef Málek
We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes equations for the velocity v, coupled with a diffusive variant of a combination of the Oldroyd-B and the Giesekus models for a tensor 𝔹. By a proper choice of the constitutive
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Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-25 Radu Ioan Boţ; Sorin-Mihai Grad; Dennis Meier; Mathias Staudigl
In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of trajectories towards the minimum norm solution of the underlying monotone inclusion problem. To that end, we investigate in detail the asymptotic behavior of dynamical systems
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Convex solutions of Monge-Ampère equations and systems: Existence, uniqueness and asymptotic behavior Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-25 Meiqiang Feng
In this paper, the equations and systems of Monge-Ampère with parameters are considered. We first show the uniqueness of of nontrivial radial convex solution of Monge-Ampère equations by using sharp estimates. Then we analyze the existence and nonexistence of nontrivial radial convex solutions to Monge-Ampère systems, which includes some new ingredients in the arguments. Furthermore, the asymptotic
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On some classes of generalized Schrödinger equations Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-22 Amanda S. S. Correa Leão; Joelma Morbach; Andrelino V. Santos; João R. Santos Júnior
Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + ∑i=2m dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.
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Liouville property of fractional Lane-Emden equation in general unbounded domain Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-22 Ying Wang; Yuanhong Wei
Our purpose of this paper is to consider Liouville property for the fractional Lane-Emden equation
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Multiple solutions for critical Choquard-Kirchhoff type equations Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-22 Sihua Liang; Patrizia Pucci; Binlin Zhang
In this article, we investigate multiplicity results for Choquard-Kirchhoff type equations, with Hardy-Littlewood-Sobolev critical exponents,
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Variational formulations of steady rotational equatorial waves Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-22 Jifeng Chu; Joachim Escher
When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained
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A posteriori analysis of the spectral element discretization of a non linear heat equation Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-07 Mohamed Abdelwahed; Nejmeddine Chorfi
The paper deals with a posteriori analysis of the spectral element discretization of a non linear heat equation. The discretization is based on Euler’s backward scheme in time and spectral discretization in space. Residual error indicators related to the discretization in time and in space are defined. We prove that those indicators are upper and lower bounded by the error estimation.
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Regularity for sub-elliptic systems with VMO-coefficients in the Heisenberg group: the sub-quadratic structure case Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-07 Jialin Wang; Maochun Zhu; Shujin Gao; Dongni Liao
We consider nonlinear sub-elliptic systems with VMO-coefficients for the case 1 < p < 2 under controllable growth conditions, as well as natural growth conditions, respectively, in the Heisenberg group. On the basis of a generalization of the technique of 𝓐-harmonic approximation introduced by Duzaar-Grotowski-Kronz, and an appropriate Sobolev-Poincaré type inequality established in the Heisenberg
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Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-02 Hans-Christoph Grunau; Nobuhito Miyake; Shinya Okabe
This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth order have no positivity preserving property due to the change of sign of the fundamental solution. One has eventual local positivity for positive
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Existence results for nonlinear degenerate elliptic equations with lower order terms Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-02 Weilin Zou; Xinxin Li
In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [, , ] in some sense.
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On variational nonlinear equations with monotone operators Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-08-02 Marek Galewski
Using monotonicity methods and some variational argument we consider nonlinear problems which involve monotone potential mappings satisfying condition (S) and their strongly continuous perturbations. We investigate when functional whose minimum is obtained by a direct method of the calculus of variations satisfies the Palais-Smale condition, relate minimizing sequence and Galerkin approximaitons when
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Ground states and multiple solutions for Hamiltonian elliptic system with gradient term Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-07-30 Wen Zhang; Jian Zhang; Heilong Mi
This paper is concerned with the following nonlinear Hamiltonian elliptic system with gradient term
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Blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-07-28 Feng Binhua; Ruipeng Chen; Jiayin Liu
In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation
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Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-07-28 Xingchang Wang; Runzhang Xu
In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and asymptotic behavior of the global solution and the blowup phenomena of solution with subcritical initial
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Concentration behavior of semiclassical solutions for Hamiltonian elliptic system Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-07-17 Jian Zhang; Jianhua Chen; Quanqing Li; Wen Zhang
In this paper, we study the following nonlinear Hamiltonian elliptic system with gradient term
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Positive Solutions for Resonant (p, q)-equations with convection Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-07-17 Zhenhai Liu; Nikolaos S. Papageorgiou
We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen variable method and eventually a fixed point argument based
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Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-07-02 Shuang Liang; Shenzhou Zheng
In this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz growth. It is mainly assumed that the variable exponents p(x) satisfy the log-Hölder continuity, while the nonlinearity and underlying domain (A, Ω) is
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Solvability of an infinite system of integral equations on the real half-axis Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-06-19 Józef Banaś; Weronika Woś
The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and
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The structure of 𝓐-free measures revisited Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-06-10 D. Mitrovic; Dj. Vujadinović
We refine a recent result on the structure of measures satisfying a linear partial differential equation 𝓐μ = σ, μ, σ are Radon measures, considering the measure μ(x) = g(x)dx + μus(x̃)(μs(x̄) + dx̄) where x = (x̃,x̄) ∈ ℝk × ℝd−k, μus is a uniformly singular measure in x̃0 and the measure μs is a singular measure. We proved that for μus-a.e. x̃0 the range of the Radon-Nykodim derivative f~(x~0)=dμusd|μus|(x~0)
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Nehari-type ground state solutions for a Choquard equation with doubly critical exponents Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-05-30 Sitong Chen; Xianhua Tang; Jiuyang Wei
This paper deals with the following Choquard equation with a local nonlinear perturbation:
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Constant sign and nodal solutions for superlinear (p, q)–equations with indefinite potential and a concave boundary term Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-05-30 Nikolaos S. Papageorgiou; Youpei Zhang
We consider a nonlinear elliptic equation driven by the (p, q)–Laplacian plus an indefinite potential. The reaction is (p − 1)–superlinear and the boundary term is parametric and concave. Using variational tools from the critical point theory together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least
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On the existence of periodic oscillations for pendulum-type equations Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-05-27 J. Ángel Cid
We provide new sufficient conditions for the existence of T-periodic solutions for the ϕ-laplacian pendulum equation (ϕ(x′))′ + kx′ + a sin x = e(t), where e ∈ C͠T. Our main tool is a continuation theorem due to Capietto, Mawhin and Zanolin and we improve or complement previous results in the literature obtained in the framework of the classical, the relativistic and the curvature pendulum equations
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On isolated singularities of Kirchhoff equations Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-05-27 Huyuan Chen; Mouhamed Moustapha Fall; Binling Zhang
In this note, we study isolated singular positive solutions of Kirchhoff equation
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Weak and stationary solutions to a Cahn–Hilliard–Brinkman model with singular potentials and source terms Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-05-27 Matthias Ebenbeck; Kei Fong Lam
We study a phase field model proposed recently in the context of tumour growth. The model couples a Cahn–Hilliard–Brinkman (CHB) system with an elliptic reaction-diffusion equation for a nutrient. The fluid velocity, governed by the Brinkman law, is not solenoidal, as its divergence is a function of the nutrient and the phase field variable, i.e., solution-dependent, and frictionless boundary conditions
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Convergence Results for Elliptic Variational-Hemivariational Inequalities Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-05-27 Dong-ling Cai; Mircea Sofonea; Yi-bin Xiao
We consider an elliptic variational-hemivariational inequality 𝓟 in a reflexive Banach space, governed by a set of constraints K, a nonlinear operator A, and an element f. We associate to this inequality a sequence {𝓟n} of variational-hemivariational inequalities such that, for each n ∈ ℕ, inequality 𝓟n is obtained by perturbing the data K and A and, moreover, it contains an additional term governed
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Single peaked traveling wave solutions to a generalized μ-Novikov Equation Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-05-22 Byungsoo Moon
In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.
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Multiplicity of concentrating solutions for a class of magnetic Schrödinger-Poisson type equation Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-05-17 Yueli Liu; Xu Li; Chao Ji
In this paper, we study the following nonlinear magnetic Schrödinger-Poisson type equation
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Editorial to Volume 10 of ANA Adv. Nonlinear Anal. (IF 2.667) Pub Date : 2020-05-04 Vicenţiu D. Rădulescu
Journal Name: Advances in Nonlinear Analysis Volume: 10 Issue: 1 Pages: 1-1
Contents have been reproduced by permission of the publishers.