On orbital stability of the physical ground states of the NLS equations

Abstract

We prove orbital stability result for physical ground states of a nonlinear Schrödinger (NLS) equation in the sense that the set of these ground states is contained in the set of prescribed mass solutions which is orbital stable by the Cazenave-Lions theorem. We apply the nonlinear generalized Rayleigh quotients method which allows establishing a one-to-one correspondence between the values of the mass $m$, the frequency $\lambda$, and the action level $S$ of the physical ground states.

21 pages

References in corpus (1)

• Separating of critical points on the Nehari manifold via the nonlinear generalized Rayleigh quotients

Cited by in corpus (2)

• On global minimizers for a mass constrained problem
• Rayleigh quotients of the level set manifolds related to the nonlinear PDE