Existence and concentration of ground state solutions for Kirchhoff type equations with general nonlinearities

Abstract

In this paper, we study the following singularly perturbed Kirchhoff type equation in subcritical casewhereUnder some suitable conditions, we obtain that there exists a ground state solution of the equation concentrating at a global minimum of V in the semiclassical limit by applying some new techniques and subtle analyses. Moreover, we use Moser iteration to conquer the difficulty caused by the lack of Sobolev inequality.