Stability analysis for positive solutions for classes of semilinear elliptic boundary-value problems with nonlinear boundary conditions

被引：8

作者：

Goddard, Jerome, II ^{[1
]}

Shivaji, Ratnasingham ^{[2
]}

机构：

[1] Auburn Univ, Dept Math, Montgomery, AL 36124 USA

[2] Univ North Carolina Greensboro, Dept Math & Stat, Greensboro, NC 27402 USA

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2017年 / 147卷 / 05期

基金：

美国国家科学基金会;

关键词：

nonlinear boundary conditions; semipositone; stability; principle of linearized stability; DIFFUSIVE LOGISTIC EQUATION; SEMIPOSITONE PROBLEMS; NONNEGATIVE SOLUTIONS; INSTABILITY; DOMAINS;

D O I：

10.1017/S0308210516000408

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the stability properties of positive steady-state solutions of semilinear initial-boundary-value problems with nonlinear boundary conditions. In particular, we employ a principle of linearized stability for this class of problems to prove sufficient conditions for the stability and instability of such solutions. These results shed some light on the combined effects of the reaction term and the boundary nonlinearity on stability properties. We also discuss various examples satisfying our hypotheses for stability results in dimension 1. In particular, we provide complete bifurcation curves for positive solutions for these examples.

引用

页码：1019 / 1040

页数：22

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