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.

引用

页码：37 / 56

页数：20

共 50 条

[21] ASYMPTOTICS OF SOLUTIONS OF THE CAUCHY-PROBLEM FOR SINGULARLY PERTURBED SYSTEMS
SHCHITOV, IN
DIFFERENTIAL EQUATIONS, 1992, 28 (05) : 625 - 634
[22] ASYMPTOTICS OF THE SOLUTIONS TO SINGULARLY PERTURBED MULTIDIMENSIONAL INTEGRAL-EQUATIONS
RAMM, AG
SHIFRIN, EI
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 190 (03) : 667 - 677
[23] Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains
Dipierro, Serena
JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (01) : 30 - 66
[24] Pseudoholomorphic and ε-Pseudoregular Solutions of Singularly Perturbed Problems
Kachalov, V., I
DIFFERENTIAL EQUATIONS, 2022, 58 (03) : 357 - 366
[25] Existence and concentration of ground state solutions for singularly perturbed nonlocal elliptic problems
Dengfeng Lü
Monatshefte für Mathematik, 2017, 182 : 335 - 358
[26] Existence and concentration of ground state solutions for singularly perturbed nonlocal elliptic problems
Lu, Dengfeng
MONATSHEFTE FUR MATHEMATIK, 2017, 182 (02): : 335 - 358
[27] Multipeak solutions for some singularly perturbed nonlinear elliptic problems on Riemannian manifolds
E. N. Dancer
A. M. Micheletti
A. Pistoia
manuscripta mathematica, 2009, 128 : 163 - 193
[28] Profile of solutions with sharp layers to some singularly perturbed quasilinear Dirichlet problems
Guo, ZM
Webb, JRL
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2003, 5 (06) : 883 - 920
[29] Multipeak solutions for some singularly perturbed nonlinear elliptic problems on Riemannian manifolds
Dancer, E. N.
Micheletti, A. M.
Pistoia, A.
MANUSCRIPTA MATHEMATICA, 2009, 128 (02) : 163 - 193
[30] 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

← 1 2 3 4 5 →