MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS

doi:10.1016/S0252-9602(10)60117-8

Abstract

Abstract:

We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schr\"odinger system in R^N. We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε sufficiently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.

Key words: Elliptic system, Schr\"odinger equation, variational methods, Nehari manifold, relative category, concentration

CLC Number:

35J50

WAN You-Yan. MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS[J].Acta mathematica scientia,Series B, 2010, 30(4): 1199-1218.

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