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

Abstract In this paper we consider the nonlinear fractional logarithmic Schrodinger 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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