Existence of three solutions for a Neumann problem involving the p(x)‐Laplace operator

In this paper, we study the existence of three solutions to a Neumann problem with nonstandard growth conditions. The technical approach is mainly based on three critical points theorem due to Ricceri. Copyright © 2011 John Wiley & Sons, Ltd.     

Second order regularity for the p(x)‐Laplace operator

In this paper, we establish second order regularity for the p(x)‐Laplace operator. This generalizes classical results known when the function p(.) is equal to some constant p > 1. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Multiplicity results for elliptic problems with variable exponent and nonhomogeneous Neumann conditions

Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p(x)‐Laplacian and subject to small perturbations of nonhomogeneous Neumann conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple solutions for a Robin‐type differential inclusion problem involving the p(x)‐Laplacian

In this paper, we obtain the existence of at least two nontrivial solutions for a Robin‐type differential inclusion problem involving p(x)‐Laplacian type operator and nonsmooth potentials. Our approach is variational, and it is based on the nonsmooth critical point theory for locally Lipschitz functions. Copyright © 2013 John Wiley & Sons, Ltd.     

Infinitely many weak solutions for p(x)-Laplacian-like problems with Neumann condition

The paper studies the existence of infinitely many solutions for a Neumann problem involving the p(x)-Laplacian-like depending on two parameters. Our approach is based on variational methods.     

Existence result for a gradient-type elliptic system involving a pair of p(x) and q(x)-Laplacian operators

In this paper, we deal with a typical gradient elliptic system involving a pair of p(x) and q(x)-Laplacian operators. Furthermore, the system may have nonlinearities with sign-changing. Precisely, we are interested in seeking at least one weak nontrivial solution. In this way, we establish explicitly a pair of lower and upper solutions having radial forms and related to the system. By applying the theory of monotone operators, we show that the system possesses at least one non-trivial and bounded solution.     

Existence and multiplicity of the solutions of the p(x)–Kirchhoff type equation via genus theory

In this paper, by using variational approach and Krasnoselskii's genus theory, we show the existence and multiplicity of the solutions of the p(x)‐Kirchhoff type equation. Copyright © 2011 John Wiley & Sons, Ltd.     

Multiple solutions to a class of inclusion problem with the p(x)-Laplacian

In this article, we obtain the existence of at least two nontrivial solutions for a nonlinear elliptic problem involving p(x)-Laplacian type operator and nonsmooth potentials. Our approach is variational and it is based on the nonsmooth critical point theory for locally Lipschitz functions.     

A critical Kirchhoff‐type problem involving the ‐Laplacian

In this paper we provide an existence result for a nonlocal problem of Kirchhoff‐type which involves both the p‐ and the q‐Laplacian and contains a critical term. Our approach is variational: we derive the existence of one non‐trivial solution via the multidimensional mountain pass theorem.     

On a bi-nonlocal p(x)-Kirchhoff equation via Krasnoselskii's genus

We study existence and multiplicity of solutions to the following bi-nonlocal p(x)-Kirchhoff equation via Krasnoselskii's genus, on the Sobolev space with variable exponent, where Ω is a bounded smooth domain of I R^N, 1 < p(x) < N, M and f are continuous functions, f is an odd function, and r > 0 is a real parameter. Copyright © 2014 John Wiley & Sons, Ltd.     

R~N上一类p(x)-Laplacian方程的无穷多解问题

该文主要讨论了如下p(x)-Laplacian算子方程的解.其中1P-≤p(x)≤P+N.得到了上述方程在变指数Sobolev空间W~(1,p(x))(R~N)中的一列能量值趋向正无穷的解.     

Infinitely many solutions for nonlocal elliptic systems of (p1(x),⋯,pn(x))‐Kirchhoff type

In this paper, we obtain the existence of infinitely solutions for a class of nonlocal elliptic systems of (p₁(x),?,p_n(x))‐Kirchhoff type. Our main results are new. Our approach are based on general variational principle because of B. Ricceri and the theory of the variable exponent Sobolev spaces. Copyright © 2015 John Wiley & Sons, Ltd.     

Hölder regularity of the gradient for the non‐homogeneous parabolic p(x,t)‐Laplacian equations

In this paper, we obtain the local Hölder regularity of the gradient of weak solutions for the non‐homogeneous parabolic p(x,t)‐Laplacian equations provided p(x,t), A and f are Hölder continuous functions. Copyright © 2013 John Wiley & Sons, Ltd.     

含p(x)-Laplacian算子的Neumann问题解的存在性

利用极大单调算子理论,给出了一类含p(x)-Laplacian算子的Neumann边值问题解的存在的充分条件.讨论用到了Lp(x)(Ω)和W01,p(x)(Ω)空间的理论.     

一类有界区域上p(X)-Laplace方程解的存在性

在变指数Lebesgue空间Lp(x)(Ω)、变指数Sobolev空间W~1,p(x)(Ω)、加权变指数Lebesgue空间Lp(x)(Ω;|x~(α(x)))和加权变指数Sobolev空间W~1,p(x)(Ω;|x|~(a(x)))的基本理论体系的基础上利用山路引理得到一类p(x)-Laplace方程非平凡解的存在性.     

Existence results for asymmetric fractional ‐Laplacian problem

We investigated a class of quasi‐linear nonlocal problems with a right‐hand side nonlinearity which exhibits an asymmetric growth at and . Namely, it is linear at and superlinear at . However, it needs not satisfy the Ambrosetti–Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by using variational methods combined with the Moser–Trudinger inequality.