EXISTENCE OF MULTIPLE WEAK SOLUTIONS FOR A QUASI-LINEAR ELLIPTIC EQUATION CONTAINING p(x)-LAPLACIAN WITH MIXED BOUNDARY CONDITIONS

Abstract

In this paper, we consider a mixed boundary value problem to a p(x)- Laplacian equation. More precisely we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary
condition on an another part of the boundary. We show the existence of at least two nontrivial weak solutions under some hypotheses on the data and parameters.