ON S-SHAPED BIFURCATION CURVES FOR A TWO-POINT BOUNDARY VALUE PROBLEM ARISING IN A THEORY OF THERMAL EXPLOSION

被引：15

作者：

Huang, Shao-Yuan ^{[1
]}

Wang, Shin-Hwa ^{[1
]}

机构：

[1] Natl Tsing Hua Univ, Dept Math, Hsinchu 300, Taiwan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 10期

关键词：

Positive solution; exact multiplicity; S-shaped bifurcation curve; turning point; Sturm's theorem; POSITIVE SOLUTIONS; POSITONE PROBLEM; NONLINEARITY; MULTIPLICITY; EQUATION; NUMBER;

D O I：

10.3934/dcds.2015.35.4839

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the bifurcation curve and exact multiplicity of positive solutions of a two-point boundary value problem arising in a theory of thermal explosion [GRAPHICS] where lambda > 0 is the Frank Kamenetskii parameter and alpha > 0 is the activation energy parameter. By developing some new time-map techniques and applying Sturm's theorem, we prove that, if alpha >= alpha ** approximate to 4.107, the bifurcation curve is S-shaped on the (lambda, parallel to u parallel to(infinity))-plane. Our result improves one of the main results in Hung and Wang (J. Differential Equations 251 (2011) 223-237).

引用

页码：4839 / 4858

页数：20

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