Multi-bump solutions for a Kirchhoff-type problem

Abstract

In this paper, we study the existence of solutions for the Kirchhoff [EQUATION PRESANTED]? Assuming that the nonnegative function a(x) has a potential well with int (a»-1({0})) consisting of k disjoint components Ω1,Ω2,...,Ωk and the nonlinearity f(t) has a subcritical growth, we are able to establish the existence of positive multi-bump solutions by using variational methods.