Three critical solutions for variational - hemivariational inequalities involving p(x)-Kirchhoff type equation

Abstract

In this paper, we study the existence of three solutions to the p(x)-Kirchhoff type equations in R^N.  By means of nonsmooth three critical points theorem and the theory of the variable exponent Sobolev spaces, we establish  the existence of three critical points  for the problem. Moreover, we study the existence of three radially symmetric solutions for a class of quasilinear elliptic inclusion problem with discontinuous nonlinearities in  R^N.  Our approach is based on critical point theory for locally Lipschitz functionals due to Iannizzotto.