FRICTIONAL CONTACT PROBLEMS INVOLVING P(X)-LAPLACIAN-LIKE OPERATORS

FRICTIONAL CONTACT PROBLEMS INVOLVING P(X)-LAPLACIAN-LIKE OPERATORS

E. C. Lapa

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Abstract

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

Keywords

p(x)- Kirchho  type equation; weak solutions; existence and uniqueness of solutions; variable exponents; frictional contact condition; Schauder  xed point theorem.