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arXiv · 1403.2176

Multiple normalized solutions for quasi-linear Schr\"odinger equations

Louis Jeanjean·Tingjian Luo·Zhi-Qiang Wang
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Abstract

In this paper we prove the existence of two solutions having a prescribed $L^2$-norm for a quasi-linear Schr\"odinger 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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Louis Jeanjean, Tingjian Luo, Zhi-Qiang Wang. 2014-03-10. Multiple normalized solutions for quasi-linear Schr\"odinger equations. https://arxiv.org/abs/1403.2176

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