Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition

被引：15
|
作者：
Liu, Ping [1 ]
Shi, Junping [2 ]
机构：
[1] Harbin Normal Univ, Sch Math Sci, YY Tseng Funct Anal Res Ctr, Harbin 150025, Heilongjiang, Peoples R China
[2] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 01期
基金：
美国国家科学基金会;
关键词：
Reaction-diffusion equation; Nonlinear boundary condition; Bifurcation; Stability; LOGISTIC ELLIPTIC EQUATION; PARABOLIC PROBLEMS; DIFFERENTIAL-EQUATIONS; GLOBAL BIFURCATION; STABLE EQUILIBRIA; INCOMING FLUX; HEAT-EQUATION; BLOW-UP; STABILITY; DOMAINS;
D O I：
10.1016/j.jde.2017.09.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions. (C) 2017 Elsevier Inc. All rights reserved.
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页码：425 / 454
页数：30
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