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

页码：63 / 115

页数：53

共 50 条

[21] Singularly perturbed spectral problems with Neumann boundary conditions
Piatnitski, A.
Rybalko, A.
Rybalko, V.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2016, 61 (02) : 252 - 274
[22] On the number of nodal solutions to a singularly perturbed Neumann problem
Wei, JC
Weth, T
MANUSCRIPTA MATHEMATICA, 2005, 117 (03) : 333 - 344
[23] On the number of nodal solutions to a singularly perturbed Neumann problem
Juncheng Wei
Tobias Weth
manuscripta mathematica, 2005, 117 : 333 - 344
[24] On the Multiplicity of Nodal Solutions to a Singularly Perturbed Neumann Problem
Anna Maria Micheletti
Angela Pistoia
Mediterranean Journal of Mathematics, 2008, 5 : 285 - 294
[25] On the Multiplicity of Nodal Solutions to a Singularly Perturbed Neumann Problem
Micheletti, Anna Maria
Pistoia, Angela
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2008, 5 (03) : 285 - 294
[26] TRIPLE JUNCTION SOLUTIONS FOR A SINGULARLY PERTURBED NEUMANN PROBLEM
Ao, Weiwei
Musso, Monica
Wei, Juncheng
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2011, 43 (06) : 2519 - 2541
[27] ANALYTICAL SOLUTIONS OF SINGULARLY PERTURBED PROBLEMS
LOMOV, SA
DOKLADY AKADEMII NAUK SSSR, 1982, 265 (03): : 529 - 533
[28] Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem
Mahmoudi, Fethi
Malchiodi, Andrea
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2006, 17 (03) : 279 - 290
[29] On the existence of symmetric solutions to some singularly perturbed semilinear elliptic problems
Pistoia, A
ASYMPTOTIC ANALYSIS, 2000, 22 (02) : 149 - 161
[30] ASYMPTOTIC REPRESENTATION OF THE SOLUTIONS OF SOME SINGULARLY PERTURBED BOUNDARY-PROBLEMS
ABDUVALIEV, AO
ROZOV, NK
SUSHKO, VG
DOKLADY AKADEMII NAUK SSSR, 1989, 304 (04): : 777 - 780

← 1 2 3 4 5 →