ON EXISTENCE OF THREE SOLUTIONS FOR $p(x)$-KIRCHHOFF TYPE DIFFERENTIAL INCLUSION PROBLEM VIA NONSMOOTH CRITICAL POINT THEORY

Abstract

In this paper, we study a class of differential inclusion problems driven by the $p(x)$-Kirchhoff with non-standard growth depending on a real parameter. Working within the framework of variable exponent spaces, a new existence result of at least three solutions for the considered problem is established by using the nonsmooth version three critical points theorem.