Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions

被引：13
|
作者：
Azorero, Jesus Garcia [2 ]
Malchiodi, Andrea [1 ]
Montoro, Luigi [3 ]
Peral, Ireneo [2 ]
机构：
[1] SISSA, I-34014 Trieste, Italy
[2] UAM, Dept Matemat, Madrid 28049, Spain
[3] UNICAL, Dipartimento Matemat, I-87036 Cosenza, Italy
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2010年 / 27卷 / 01期
关键词：
Singularly perturbed elliptic problems; Finite-dimensional reductions; Local inversion; SEMILINEAR NEUMANN PROBLEM; POSITIVE SOLUTIONS;
D O I：
10.1016/j.anihpc.2009.06.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
this paper we carry on the study of asymptotic behavior of some Solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper [J. Garcia Azorero, A. Malchiodi. L. Montoro, I. Peral, Concentration of solutions for some singularly perturbed mixed problems: Existence results, Arch. Ration. Mech. Anal., in press]. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular Perturbation parameter tends to zero. We show that in many cases they coincide with the new Solutions produced in [J. Garcia Azorero. A. Malchiodi, L. Montoro. I. Peral, Concentration of solutions for some singularly perturbed mixed problems: Existence results, Arch. Ration. Mech. Anal., in press]. (C) 2009 Elsevier Masson SAS. All rights reserved.
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页码：37 / 56
页数：20
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