Logarithmic NLS equation on star graphs: existence and stability of standing waves

2016/11/30 by Alex H. Ardila · 1 citation
Mathematics · #math.AP

paper · pdf

published as Differential Integral Equations. Volume 30, Number 9/10 (2017), 735-762 · 22 pages. arXiv admin note: text overlap with arXiv:1608.06929

arxiv created 2017/10/31 · arxiv updated 2017/11/02

Abstract

In this paper we consider the logarithmic Schrödinger equation on a star graph. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. Then we show the existence of several families of standing waves. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we show that the ground states are orbitally stable via a variational approach.

Citations

• Stability of ground states for logarithmic Schrödinger equation with a δ^′-interaction

Cited by

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

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