Multiplicity of self-similar solutions for a critical equation

被引：18
|
作者：
Furtado, Marcelo F. [1 ]
da Silva, Joao Pablo P. [2 ]
Xavier, Magda S. [3 ]
机构：
[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil
[2] Fed Univ Para, Dept Matemat, BR-66075110 Belem, PA, Brazil
[3] Univ Fed Espirito Santo, Dept Matemat, BR-29075910 Vitoria, ES, Brazil
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 254卷 / 07期
关键词：
Critical problems; Symmetric functionals; Self-similar solutions; CRITICAL SOBOLEV EXPONENTS; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS;
D O I：
10.1016/j.jde.2013.01.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the equation -Delta u-1/2(x.del u) = f(u) + beta vertical bar u vertical bar(2*-2)u, x is an element of R-N, with beta > 0, f superlinear and 2* := 2N/(N-2) for N >= 3. We prove that, for each k is an element of N, there exists beta* = beta* (k) > 0 such that the equation has at least k pairs of solutions provided beta is an element of (0, beta*). In the proof we use variational methods for the (even) functional associated to the equation. (C) 2013 Published by Elsevier Inc.
引用
收藏
页码：2732 / 2743
页数：12
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