Open Access Research

Existence of positive ground states for some nonlinear Schrödinger systems

Hui Zhang, Junxiang Xu* and Fubao Zhang

Author Affiliations

Department of Mathematics, Southeast University, Nanjing, 210096, P.R. China

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Boundary Value Problems 2013, 2013:13 doi:10.1186/1687-2770-2013-13

Published: 28 January 2013

Abstract

We prove the existence of positive ground states for the nonlinear Schrödinger system

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/13/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/13/mathml/M1">View MathML</a>

where a, b are periodic or asymptotically periodic and F satisfies some superlinear conditions in <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/13/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/13/mathml/M2">View MathML</a>. The proof is based on the method of Nehari manifold and the concentration-compactness principle.

MSC: 35J05, 35J50, 35J61.

Keywords:
nonlinear Schrödinger system; Nehari manifold; lack of compactness; ground state