Asymptotic behaviour of a semilinear elliptic system with a large exponent

被引：2

作者：

Guerra, I. A. ^{[1
]}

机构：

[1] Univ Santiago Chile, Dept Matemat & CC, Santiago, Chile

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2007年 / 19卷 / 01期

关键词：

semilinear elliptic system; asymptotic behaviour; peaks;

D O I：

10.1007/s10884-006-9045-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider the problem -Delta u = v(2/N-2), v > 0 in Omega, -Delta v = u(p), u > 0 in Omega, u = v = 0 on partial derivative Omega, where Omega is a bounded convex domain in R-N N > 2, with smooth boundary partial derivative Omega. We study the asymptotic behaviour of the least energy solutions of this system as p -> infinity . We show that the solution remain bounded for p large. In the limit, we find that the solution develops one or two peaks away from the boundary, and when a single peak occurs, we have a characterization of its location.

引用

页码：243 / 263

页数：21

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