Abstract
In this paper we show multiplicity of solutions for a parameterized quasilinear Schrödinger equation in the presence of a square diffusion and indefinite superlinear term. Due to the presence of the quasilinear term, we can no longer work on the standard Sobolev spaces to show existence and non-existence of solutions. We overcome these difficulties by using perturbations arguments, Nehari sets and nonlinear Rayleigh quotients. As a byproduct of this approach we show that the associated energy functional has non-zero global minimizers only for small parameters.
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