Positive and sign-changing solutions for nonlinear equations with rapid growing weights

被引：1

作者：

Figueiredo, Giovany ^{[1
]}

Montenegro, Marcelo ^{[2
]}

机构：

[1] Univ Brasilia, Dept Matemat, Brasilia, DF, Brazil

[2] Univ Estadual Campinas, Dept Matemat, IMECC, Campinas, SP, Brazil

来源：

APPLICABLE ANALYSIS | 2023年 / 102卷 / 06期

基金：

巴西圣保罗研究基金会;

关键词：

Subcritical and critical equation; exponential weights; self-similar solutions; ground state; positive solution; nodal domain; sign-changing solution; weak solutions; SELF-SIMILAR SOLUTIONS; ELLIPTIC-EQUATIONS; MULTIPLICITY;

D O I：

10.1080/00036811.2021.1998462

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of a positive ground state and a sign-changing solution with exactly two nodal domains for the equation -div(K(x)del u) = lambda Kx)vertical bar x vertical bar(beta)vertical bar u vertical bar(q-2)u+gamma K(x)vertical bar u vertical bar(2)*(-2) u in R-N, where N >= 3, 2 < q < 2N/(N = 2), lambda > 0 is a parameter, K(x) = exp(vertical bar x vertical bar(alpha)/4), alpha >= 2 and beta = (alpha - 2) (2*-q/2*-2). The equation is subcritical if gamma = 0 and critical if gamma = 1.

引用

页码：1687 / 1695

页数：9

共 21 条

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