Concentration of Solutions for Some Singularly Perturbed Neumann Problems

被引：2
|
作者：
Malchiodi, Andrea [1 ]
机构：
[1] SISSA, Sector Math Anal, I-34014 Trieste, Italy
来源：
GEOMETRIC ANALYSIS AND PDES | 2009年 / 1977卷
关键词：
NONLINEAR SCHRODINGER-EQUATIONS; BOUNDARY PEAK SOLUTIONS; MULTIPEAK SOLUTIONS; SEMICLASSICAL STATES; ELLIPTIC-EQUATIONS; LAYER SOLUTIONS; GROUND-STATES; EXISTENCE; STABILITY; INTERIOR;
D O I：
10.1007/978-3-642-01674-5_3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The purpose of these notes is to present some techniques for constructing solutions to a class of singularly perturbed problems with a precise asymptotic behavior when the perturbation parameter ε tends to zero. We first treat the case of concentration at points, and then the case of concentration at manifolds. One of the main motivations for the study of these equations arises from reaction-diffusion systems, concerning in particular the so-called Turing's instability. © 2009 Springer-Verlag Berlin Heidelberg.
引用
收藏
页码：63 / 115
页数：53
相关论文
共 50 条
  • [1] Nodal Clustered Solutions for Some Singularly Perturbed Neumann Problems
    D'Aprile, Teresa
    Pistoia, Angela
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (08) : 1355 - 1401
  • [2] Multiple interior peak solutions for some singularly perturbed Neumann problems
    Gui, CF
    Wei, JC
    JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 158 (01) : 1 - 27
  • [3] Multiple boundary peak solutions for some singularly perturbed Neumann problems
    Gui, CF
    Wei, JC
    Winter, M
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2000, 17 (01): : 47 - 82
  • [4] Multiplicity of multiple interior peak solutions for some singularly perturbed Neumann problems
    Cerami, G
    Wei, JC
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 1998, 1998 (12) : 601 - 626
  • [5] Concentration of Solutions for Some Singularly Perturbed Mixed Problems: Existence Results
    Jesus Garcia Azorero
    Andrea Malchiodi
    Luigi Montoro
    Ireneo Peral
    Archive for Rational Mechanics and Analysis, 2010, 196 : 907 - 950
  • [6] Concentration of Solutions for Some Singularly Perturbed Mixed Problems: Existence Results
    Garcia Azorero, Jesus
    Malchiodi, Andrea
    Montoro, Luigi
    Peral, Ireneo
    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 196 (03) : 907 - 950
  • [7] On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems
    Gui, CF
    Wei, JC
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2000, 52 (03): : 522 - 538
  • [8] ON SOLVING SEMILINEAR SINGULARLY PERTURBED NEUMANN PROBLEMS FOR MULTIPLE SOLUTIONS*
    Xie, Ziqing
    Yuan, Yongjun
    Zhou, Jianxin
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2022, 44 (01): : A501 - A523
  • [9] Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions
    Azorero, Jesus Garcia
    Malchiodi, Andrea
    Montoro, Luigi
    Peral, Ireneo
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (01): : 37 - 56
  • [10] On the role of mean curvature in some singularly perturbed Neumann problems
    Del Pino, M
    Felmer, PL
    Wei, JC
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1999, 31 (01) : 63 - 79
12345