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Existence and stability of standing waves to Schrödinger-Poisson equations with harmonic potential

Abstract

In this talk, we will discuss the existence and stability of standing waves to a class of  Schrödinger-Poisson equation with harmonic potential. To establish the existence result, we will employ a variant of mountain pass theorem. With regard to the stability, Lyapunov-Schmidt reduction procedure and operator spectrum analysis are introduced.


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