Existence of solution for a Dirichlet boundary value problem involving the p(x) Laplacian via a fixed point approach

Miskolc Mathematical Notes

article

Souad Ayadi¹  Ozgur Ege² 

[1] Science Department of Matter, Faculty of Science, Djilali Bounaama University;Ege University, Faculty of Science, Department of Mathematics

关键词: p(x)-Laplacian;    generalized Sobolev space;    variable exponent;    fixed point;   

DOI  :  10.18514/MMN.2022.4101

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

In this paper, we study the existence of a non-trivial solution in $W_{0}^{1,p(x)}(\Omega)$ for the problem $$\begin{cases}\Delta_{p(x)}u=f(x,u,\nabla u) \;\;{\rm in}\quad \Omega,\\ u=0\;\;{\rm in}\quad \Omega.\end{cases}$$ The proof is based on Schaefer's fixed point theorem.

【 授权许可】

CC BY