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

  • Souad Ayadi, Science Department of Matter, Faculty of Science, Djilali Bounaama University, Khemis Miliana, Algeria,
  • Ozgur Ege, Ege University, Faculty of Science, Department of Mathematics, Bornova, 35100, Izmir, Turkey,


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.

Vol. 23 (2022), No. 1, pp. 85-92
DOI: 10.18514/MMN.2022.4101

Download: MMN-4101