Solutions for quasilinear Schrödinger equation on involving indefinite potentials

Abstract

This paper is concerned with the quasilinear Schrödinger equation where , V is a given potential allowed to be indefinite, or equivalently, the Schrödinger operator can be indefinite. We consider the case that V is coercive so that the working space can be compactly embedded into Lebesgue spaces. Using the local linking theorem and Morse theory, we obtain a nontrivial solution for the above problem. Moreover, by the symmetric mountain pass theorem, we get an unbounded sequence of solutions.