Multiplicity and concentration behaviour of positive solutions for Schrödinger-Kirchhoff type equations involving the p-Laplacian in [formula omitted

Abstract

In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrödinger-Kirchhoff type -∈p M(∈p-N∫RN|∇u|p)Δpu+V(x)|u|p-2u=f(u)in RN, where Δp is the p-Laplacian operator, 1 <p <N, M: R+→R+ and V: RN→R+ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik-Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.