Morse index and critical/super-critical Dirichlet problems with a large parameter

被引：0

作者：

Petralla, Maristella ^{[1
]}

机构：

[1] Univ Roma Tre, Dipartimento Matemat, I-00146 Rome, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2013年 / 76卷

关键词：

Blow-up; Morse index; Critical exponent; SEMILINEAR ELLIPTIC-EQUATIONS; BOUNDED-ENERGY;

D O I：

10.1016/j.na.2012.07.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Dirichlet problem {-Delta u + lambda u = u(p) in ohm u = 0 on partial derivative ohm, (1) with ohm subset of R-N, N >= 3, a bounded domain, with p >= N vertical bar 2/N 2, in the regime lambda -> +infinity. In this paper, we study the asymptotic behavior of positive solutions of (1) and we obtain that solutions of (1) cannot have uniformly bounded Morse index as lambda -> +infinity as long as p < p(JL)( N), the so-called Joseph-Lundgren exponent. (c) 2012 Elsevier Ltd. All rights reserved.

引用

页码：14 / 40

页数：27