On the Frictional Contact Problem of p(x)-Kirchhoff Type

Abstract

In this article we consider a class of frictional contact problem of p(x)-Kirchhoff type, on a bounded domain Ω⊆R2. Using an abstract Lagrange multiplier technique and the Schauder’s fixed point theorem we establish the existence of weak solutions. Furthermore, we also obtain the uniqueness of the solution assuming that the datum f1 satisfies a suitable monotonicity condition.