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.     

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 solutions for polyharmonic equations of p(x)-Laplace type

We show the existence of infinitely many weak solutions to a class of quasilinear elliptic p(x)-polyharmonic Kirchhoff equations via the mountain pass principle without the (AR) condition. Furthermore, we obtain infinitely many solutions to this equation based on the genus theory, introduced by Krasnoselskii and the abstract critical point theorem (a variant of Ljusternik-Schnirelman theory) under Cerami condition.     

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.     

Two positive solutions for a Dirichlet problem with the (p,q)-Laplacian

The aim of this paper is to prove the existence of two solutions for a nonlinear elliptic problem involving the $(p,q)$-Laplacian operator. The solutions are obtained by using variational methods and critical points theorems. The positivity of the solutions is shown by applying a generalized version of the strong maximum principle.     

Three solutions for a differential inclusion problem involving the -Laplacian

In this paper we consider differential inclusion problem involving the p(x)-Laplacian of the type

Applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in .     

Existence results for a class of nonlocal problems involving p(x)‐Laplacian

This paper is concerned with the existence of solutions to a class of p(x)‐Kirchhoff‐type equations with Dirichlet boundary data as follows: By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish some conditions on the existence of solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

含临界指数的p(x)-Laplace方程解的存在性

研究了一含临界指数的p(x)-Laplace方程的Dirichlet边值问题,运用推广的集中紧致性原理,并结合山路引理得到了该问题非平凡弱解的存在性结果.     

Existence of positive solutions of (p(x),q(x))-Laplacian parabolic systems with right hand side defined as a multiplication of two separate functions

The paper deals with the study of the existence of weak positive solutions for a new class of the system of parabolic differential equations with respect to the symmetry conditions by using sub-super solutions method. Our results are natural extensions from our previous ones in (Bol. Soc. Mat. Mex. 2019; 25:145-162) and (Appl. Math E-Notes. 2018; 18:209-218), where we have already studied the existence of positive solutions for some classes of Laplacian elliptic problems by using one classical method.     

Multiplicity results for p(x)-biharmonic equations with Navier boundary conditions

This paper deals with the existence of solutions for a class of p(x)-biharmonic equations with Navier boundary conditions. The approach is based on variational methods and critical point theory. Indeed, we investigate the existence of two solutions for the problem under some algebraic conditions with the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Moreover, by combining two algebraic conditions on the nonlinear term which guarantee the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of the third solution for the problem.     

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.     

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.     

一类带权的p(x)-Laplace方程解的存在性

利用山路引理,嵌入定理和h(o|¨)lder不等式证明了一类带权的p(x)-Laplace方程非平凡解的存在性.