A NOTE ON SIGN-CHANGING SOLUTIONS TO SUPERCRITICAL YAMABE-TYPE EQUATIONS

被引：0

作者：

Julio-batalla, Jurgen ^{[1
]}

机构：

[1] Univ Ind Santander, Bucaramanga, Colombia

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2025年 / 24卷 / 02期

关键词：

Yamabe equation; isoparametric functions; Sobolev inequalities; mountain pass theorem; nodal solutions; NODAL SOLUTIONS; ISOPARAMETRIC FUNCTIONS;

D O I：

10.3934/cpaa.2024082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

On a closed Riemannian manifold ( M-n , g ), we consider the Yamabe-type equation -triangle(g)u + hu = |u|(q-1) u , where q > 1 and h is a positive C 1- function. We assume that M admits a proper isoparametric function f with focal submanifolds of positive dimension. If k > 0 is the minimum of the dimensions of the focal submanifolds of f , we let q & lowast; = n-k +2/n-k- 2 .We prove the existence of infinite f-invariant sign-changing solutions to the equation when 1 < q < q & lowast; .

引用

页码：140 / 152

页数：13

共 28 条

[1]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[2] The second Yamabe invariant [J].