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.
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页码：14 / 40
页数：27
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