MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS

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

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1199-1218.doi: 10.1016/S0252-9602(10)60117-8

MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS

万优艳

Institute of Physics and Mathematics, the Chinese Academy of Sciences, Wuhan |430071, China; The Department of Mathematics, Jianghan University, Wuhan 430056, China

收稿日期:2008-09-12 修回日期:2008-12-18 出版日期:2010-07-20 发布日期:2010-07-20
基金资助:
Supported by CAS-KJCX3-SYW-S03, Grant Fondecyt No. 1050613, and Scientific Research Fund for Youth of Hubei Provincial Education Department (Q20083401)

MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS

WAN You-Yan

Institute of Physics and Mathematics, the Chinese Academy of Sciences, Wuhan |430071, China; The Department of Mathematics, Jianghan University, Wuhan 430056, China

Received:2008-09-12 Revised:2008-12-18 Online:2010-07-20 Published:2010-07-20
Supported by:
Supported by CAS-KJCX3-SYW-S03, Grant Fondecyt No. 1050613, and Scientific Research Fund for Youth of Hubei Provincial Education Department (Q20083401)

摘要/Abstract

摘要：

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.

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

Abstract:

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

中图分类号:

35J50

万优艳. MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS[J]. 数学物理学报(英文版), 2010, 30(4): 1199-1218.

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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MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS

MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS

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