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

页码：2732 / 2743

页数：12

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