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.
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