Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024561 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 13 Pages |
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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Authors
Alex H. Ardila,