Advances in Differential Equations

On coupled systems of Schrödinger equations

Z. Chen and W. Zou

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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703206

Mathematical Reviews number (MathSciNet)
MR2829504

Subjects
Primary: 35J60: Nonlinear elliptic equations 35J91: Semilinear elliptic equations with Laplacian, bi-Laplacian or poly- Laplacian 35J92: Quasilinear elliptic equations with p-Laplacian 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 58E30: Variational principles

Citation

Chen, Z.; Zou, W. On coupled systems of Schrödinger equations. Adv. Differential Equations 16 (2011), no. 7/8, 775--800. https://projecteuclid.org/euclid.ade/1355703206.


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