MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
THREE WEAK SOLUTIONS FOR A $\boldsymbol{p(x)}$-LAPLACIAN EQUATION
M. Alimohammady, A. Rezvani, I. Aydin

Abstract

We study the existence of three weak solutions to the Dirichlet boundary condition for a $p(x)$-Laplacian equation. Using a variational method and the three critical point theorem, we would show the existence and multiplicity of the solutions. For this purpose, we focus on a generalized variable exponent Lebesgue-Sobolev space.

Creative Commons License

Keywords: $p(x)$-Laplacian; variational method; three solutions; Sobolev space.

MSC: 35A15, 35J35, 46E35

DOI: 10.57016/MV-HBUM1359

Pages:  1--7