Weak solvability via Lagrange multipliers for Frictional antiplane contact problems of p(x)-Kirchhoff type

This paper is concerned with the existence and uniqueness of solutions for a class of frictional antiplane contact problems of p(x)-Kirchhoff type on a bounded domain of R۲. Using an abstract Lagrange multiplier technique and the Schauder fixed point theorem we establish the existence of weak solutions. Imposingsome suitable monotonicity conditions on the datum f۱ the uniqueness of the solution is obtained.

Keywords:

frictional antiplane contact problems , p(x)-Kirchhoff equation , Schauder fixed point theorem , uniqueness