EXISTENCE OF THREE WEAK SOLUTIONS FOR THE KIRCHHOFF-TYPE PROBLEM WITH MIXED BOUNDARY CONDITION IN A VARIABLE SOBOLEV SPACE

Abstract

In this paper, we consider the Kirchhoff-type problem for a class of nonlinear operators containing p(·)-Laplacian and mean curvature operator with mixed boundary conditions. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions according to hypotheses on given functions and values of parameters.