Advances in Differential Equations

On coupled systems of Schrödinger equations

Abstract

In this paper we study the following system of nonlinear Schrödinger equations: $$\begin{cases}-\Delta u +u = f(x,u)+\lambda v, & x\in \mathbb R^N,\\ -\Delta v +v =g(x,v)+\lambda u, & x\in \mathbb R^N.\end{cases}$$ Under some assumptions on $f$ and $g$, we obtain the existence of positive ground and bound states of the coupled system for $\lambda \in (0, 1)$. More importantly, we will give more precise descriptions of the limit behavior and energy estimates of the bound states as $\lambda$ changes.

Article information

Source
Adv. Differential Equations Volume 16, Number 7/8 (2011), 775-800.

Dates
First available in Project Euclid: 17 December 2012

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