Dirichlet boundary value problem related to the p(x)-Laplacian with discontinuous nonlinearity

2019/11/04 by Mustapha Ait Hammou, Hammou, Mustapha Ait
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1911.01252

openalex publication_date 2019/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to the p(x)-Laplacian -div(|∇ u|^p(x)-2∇ u)+u∈ -[\underlineg(x,u),g(x,u)], by using the degree theory after turning the problem into a Hammerstein equation. The right hand side g is a possibly discontinuous function in the second variable satisfying some non-standard growth conditions..

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