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MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRDINGER SYSTEMS 被引量：1

MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRDINGER SYSTEMS
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摘要 We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger 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 suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function. We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger 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 suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.
作者 万优艳
机构地区 Institute of Physics and Mathematics The Department of Mathematics
出处 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1199-1218,共20页 数学物理学报（B辑英文版）
基金 Supported by CAS-KJCX3-SYW-S03,Grant Fondecyt No. 1050613 Scientific Research Fund for Youth of Hubei Provincial Education Department(Q20083401)
关键词 Elliptic system Schrdinger equation variational methods Nehari manifold relative category CONCENTRATION Elliptic system Schrdinger equation variational methods Nehari manifold relative category concentration
分类号 O189.1 [理学—基础数学]
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参考文献19

  • 1Alves C O, Soares S H M. Singularly perturbed elliptic systems. Nonlinear Analysis, 2006, 04:109-129.
  • 2Alves C O, Soares S H M, Yang J. On existence and concentration of solutions for a class of Hamiltonian systems in RN. Adv Nonlinear Stud, 2003, 3:161-180.
  • 3Avila A, Yang J. On the existence and shape of least energy solutions for some elliptic systems. J Diff Eq, 2003, 191:348-376.
  • 4Avila A, Yang J. Multiple solutions of nonlinear elliptic systems. NoDEA, 2006, 12:459-479.
  • 5Cingolani S, Lazzo M. Multiple positive solutions to nonlinear Schrodinger equations with competing potnetial functions. J Diff Eqns, 2000, 160:118-138.
  • 6De Figueiredo D, Felmer P. On superquadratic elliptic systems. Trans Amer Math Soc, 1994, 102:188-207.
  • 7De Figueiredo D, Yang J. Decay, symmetry and existence of solutions to semilinear elliptic systems. Nonlinear Analysis TMA, 1998, 33(3): 211-234.
  • 8Del Pino M, Felmer P. Semi-classical states of nonlinear Schrodinger equations: a variational reduction method. Math Ann, 2002, 324:1-32.
  • 9Hulshof J, Van der Vorst R. Differential systems with strongly indefinite variational sturcture. J Funct Anal, 1993, 114:32-58.
  • 10Lions P. The concentration-compactness principle in the calculus of variations. The locally compact case part 1 and 2. Ann Inst H Poincare Anal Non Lineaire, 1984, 1: 109-145; 223-283.

同被引文献14

  • 1Wan Youyan, Yang Jianfu. Multiple solutions for inhomo- geneous critical semilinear elliptic problems[J]. NonlinearAnalysis:Theory, Methods & Applications, 2008, 68 (9) : 2569-2593.
  • 2Brezis H, Nirenberg L. Positive solutions of nonlinear elliptic equation involving critical Sobolev exponents [J]. Comm Pure Appl Math, 1983, 36(4) :437-477.
  • 3TaranteUo G. On nonhomogeneous elliptic equations involving critical Sobolev exponent[J]. Ann Inst H Poincare Anal Nonli, 1992, 9(3) :281-304.
  • 4Passaseo D. Some sufficient conditions for the existence of 2'-1. positive solutions to the equation -Au + a(x)u = u m bounded domains[J]. Ann Inst H Poincare Anal Nonli, 1996, 13(2) : 185-227.
  • 5Adachi S, Tanaka K. Four positive solutions for the semi- N linear elliptic equation: -Au + u = a(x)up +f(x) in R [J]. Calculus of Variations and Partial Differential Equations, 2000, 11(1):63-95.
  • 6Benci V, Cerami G. Existence of positive solutions of the N+2 N-2 N equation -Au + a(x)u = u in R [J]. J Funct Anal, 1990, 88(1):90-117.
  • 7Wan Youyan. Existence and concentration of positive solu- tions for coupled nonlinear Schrodinger systems in RN [J]. Adv Nonlinear Stud, 2007, 7 : 77-95.
  • 8Wan Youyan, Avila A I. Multiple solutions of a coupled nonlinear Schr0dinger system[J]. J Math Anal Appl, 2007, 334(2) : 1308-1325.
  • 9Alves C O, Soares S H M. Singularly perturbed elliptic systems[J]. Nonlinear Analysis:Theory, Methods & Appli- cations, 2006, 64(1) : 109-129.
  • 10Alves C O, Soares S H M, Yang J. On existence and con- centration of solutions for a class of Hamiltonian systems in RN [J]. Adv Nonlinear Stud, 2003, 3:161-180.

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Acta Mathematica Scientia
2010年 第4期

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