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