Nodal solutions of quasilinear Schrödinger equations in $\mathbb R^N$

Abstract

In this paper, we consider the existence of stationary solutions to a class of quasilinear Schrödinger type equations. As a main novelty with respect to previous results, we are able to deal with locally super-linear nonlinearities in a fairly general framework and prove the existence of finite energy nodal solutions. The proof is accomplished by a new variational perturbation approach together with a delicate analysis of the asymptotic behavior of descending flow.