Nondegenerate solutions for constrained semilinear elliptic problems on Riemannian manifolds

被引：1

作者：

Ramos, Gustavo de Paula ^{[1
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2021年 / 28卷 / 06期

关键词：

Nondegenerate critical points; Generic result; Singular perturbation; Semilinear elliptic equation; GENERIC PROPERTIES;

D O I：

10.1007/s00030-021-00726-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M-n be a connected compact smooth manifold, where n >= 2. In this article, we prove that nondegeneracy of nonconstant solutions for a class of singularly perturbed semilinear elliptic problems on M is generic with respect to the pair (epsilon, g), where epsilon > 0 and g is a metric of class C-k, k >= 1. As applications, we show that under certain growth conditions, such result generalizes to nondegeneracy of any solution for the Allen-Cahn or nonlinear Schrodinger equations.

引用

页数：11

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