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arXiv · 1701.01363

Existence and stability of standing waves for nonlinear fractional Schrödinger equation with logarithmic nonlinearity

Alex Hernandez Ardila
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Abstract

In this paper we consider the nonlinear fractional logarithmic Schrödinger equation. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we prove that the set of minimizers is a stable set for the initial value problem, that is, a solution whose initial data is near the set will remain near it for all time.

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Alex Hernandez Ardila. 2017-01-20. Existence and stability of standing waves for nonlinear fractional Schrödinger equation with logarithmic nonlinearity. https://doi.org/10.1016/j.na.2017.01.006

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