Lane-Emden problems: Asymptotic behavior of low energy nodal solutions

被引：17
作者：
Grossi, Massimo [1 ]
Grumiau, Christopher [2 ]
Pacella, Filomena [1 ]
机构：
[1] Univ Roma Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[2] Univ Mons, Inst Math, B-7000 Mons, Belgium
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2013年 / 30卷 / 01期
关键词：
Superlinear elliptic boundary value problem; Least energy nodal solution; Asymptotic behavior; Variational methods; 2-DIMENSIONAL ELLIPTIC PROBLEM; SIGN-CHANGING SOLUTIONS; QUALITATIVE PROPERTIES; LARGE EXPONENT; EQUATIONS; SYMMETRY;
D O I：
10.1016/j.anihpc.2012.06.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the nodal solutions of the Lane-Emden-Dirichlet problem {-Delta u = vertical bar u vertical bar(p-1)u, in Omega u = 0, on delta Omega, where Omega is a smooth bounded domain in R-2 and p > 1. We consider solutions u(p) satisfying p integral(Omega)vertical bar del u(p)vertical bar(2) -> 16 pi e as p -> +infinity and we are interested in the shape and the asymptotic behavior as p -> +infinity. First we prove that (*) holds for least energy nodal solutions. Then we obtain some estimates and the asymptotic profile of this kind of solutions. Finally, in some cases, we prove that pu(p) can be characterized as the difference of two Green's functions and the nodal line intersects the boundary of Omega, for large p. (C) 2012 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：121 / 140
页数：20
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