Multiple normalized solutions for quasi-linear Schrödinger equations

preprint2015arXivOpen access

Abstract

In this paper we prove the existence of two solutions having a prescribed L2L^2-norm for a quasi-linear Schrödinger equation. One of these solutions is a mountain pass solution relative to a constraint and the other one a minimum either local or global. To overcome the lack of differentiability of the associated functional, we rely on a perturbation method developed in [27].

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