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