Existence of strong solutions of a p (x) -Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition Dedicated to Prof. Xianling Fan on his 70th birthday

Qihu Zhang; Chunshan Zhao

doi:10.1016/j.camwa.2014.10.022

Existence of strong solutions of a p (x) -Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition Dedicated to Prof. Xianling Fan on his 70th birthday

Qihu Zhang, Chunshan Zhao

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

In this paper, we consider the existence of strong solutions of the following p(x)-Laplacian Dirichlet problem via critical point theory: -div( u^p(x)-2u)=f(x,u), in Ω,u=0, on Ω. We give a new growth condition, under which, we use a new method to check the Cerami compactness condition. Hence, we prove the existence of strong solutions of the problem as above without the growth condition of the well-known Ambrosetti-Rabinowitz type and also give some results about multiplicity of the solutions.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Computers and Mathematics with Applications
Volume	69
Issue number	1
DOIs	https://doi.org/10.1016/j.camwa.2014.10.022
State	Published - Jan 1 2015

Scopus Subject Areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

Keywords

Ambrosetti-Rabinowitz condition
Critical point
Dirichlet problem
Variable exponent space
Without
p (x) -Laplacian

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abstract = "In this paper, we consider the existence of strong solutions of the following p(x)-Laplacian Dirichlet problem via critical point theory: -div( up(x)-2u)=f(x,u), in Ω,u=0, on Ω. We give a new growth condition, under which, we use a new method to check the Cerami compactness condition. Hence, we prove the existence of strong solutions of the problem as above without the growth condition of the well-known Ambrosetti-Rabinowitz type and also give some results about multiplicity of the solutions.",

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AB - In this paper, we consider the existence of strong solutions of the following p(x)-Laplacian Dirichlet problem via critical point theory: -div( up(x)-2u)=f(x,u), in Ω,u=0, on Ω. We give a new growth condition, under which, we use a new method to check the Cerami compactness condition. Hence, we prove the existence of strong solutions of the problem as above without the growth condition of the well-known Ambrosetti-Rabinowitz type and also give some results about multiplicity of the solutions.

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KW - Critical point

KW - Dirichlet problem

KW - Variable exponent space

KW - Without

KW - p (x) -Laplacian

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JO - Computers and Mathematics with Applications

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IS - 1

ER -

Existence of strong solutions of a p (x) -Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition Dedicated to Prof. Xianling Fan on his 70th birthday

Abstract

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Keywords

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