Frictional contact problems involving p(x)-Laplacian-like operators

Abstract

This article is dedicated to studying a class of frictional contact problems involving the p(x)-Laplacian-like operator, on a bounded domain Ω ⊆ R². Using an abstract Lagrange multiplier technique and the Schauder fixed point theorem we establish the existence of a weak solution. Furthermore, we also obtain the uniqueness of the solution assuming that the datum f1 satisfies a suitable monotonicity condition. The results here extend earlier theorems due to Cojocaru- Matei to the quasilinear case, with semilinearity f1.