Multiplicity of self-similar solutions for a critical equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Furtado, Marcelo F.¹  da Silva, Joao Pablo P.²  Xavier, Magda S.³ 

[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

关键词: Critical problems;    Symmetric functionals;    Self-similar solutions;   

DOI  :  10.1016/j.jde.2013.01.007

来源: Elsevier

【 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.

【 授权许可】

Free