On a class of nonhomogeneous equations of Henon-type: Symmetry breaking and non radial solutions

被引：0

作者：

Assuncao, Ronaldo Brasileiro ^{[3
]}

Miyagaki, Olimpio Hiroshi ^{[1
]}

Pereira, Gilberto de Assis ^{[3
]}

Rodrigues, Bruno Mendes ^{[2
]}

机构：

[1] Univ Fed Juiz de Fora, Dept Matemat, BR-36036000 Juiz De Fora, MG, Brazil

[2] Univ Fed Ouro Preto, Dept Matemat, BR-35400000 Ouro Preto, MG, Brazil

[3] Univ Fed Minas Gerais, Dept Matemat, BR-30123970 Belo Horizonte, MG, Brazil

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 165卷

关键词：

Henon equation; Degenerate operator; Non radial solutions; POSITIVE SOLUTIONS; GROUND-STATES;

D O I：

10.1016/j.na.2017.09.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we study the following Henon-type equation {-div (|del u|(p) (2)del u/|x|(ap)) = |x|(beta)f(u), in B; u > 0, in B; u = 0, on partial derivative B; where B := {x is an element of R-N; |x| < 1} is a ball centered at the origin, the parameters verify the inequalities 0 <= a < N-p/p, N >= 4, beta > 0, 2 = p < Np+p beta/N-p(a+1), and the nonlinearity f is nonhomogeneous. By minimization on the Nehari manifold, we prove that for large values of the parameter beta there is a symmetry breaking and non radial solutions appear. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：102 / 120

页数：19

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