Existence of Strong Solutions of a P(X) -Laplacian Dirichlet Problem without the Ambrosetti-Rabinowitz Condition
Document Type
Article
Publication Date
1-2015
Publication Title
Computers & Mathematics with Applications
DOI
10.1016/j.camwa.2014.10.022
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)−2∇u)=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.
Recommended Citation
Zhang, Qihu, Chunshan Zhao.
2015.
"Existence of Strong Solutions of a P(X) -Laplacian Dirichlet Problem without the Ambrosetti-Rabinowitz Condition."
Computers & Mathematics with Applications, 69 (1): 1-12.
doi: 10.1016/j.camwa.2014.10.022
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/364
