An Evolutionary Property of the Bifurcation Curves for a Positone Problem with Cubic Nonlinearity

被引:3
|
作者
Huang, Shao-Yuan [1 ]
Wang, Shin-Hwa [1 ]
机构
[1] Natl Tsing Hua Univ, Dept Math, Hsinchu 300, Taiwan
来源
TAIWANESE JOURNAL OF MATHEMATICS | 2016年 / 20卷 / 03期
关键词
Positive solution; Exact multiplicity; Turning point; S-shaped bifurcation curve; BOUNDARY-VALUE PROBLEM;
D O I
10.11650/tjm.20.2016.6563
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study an evolutionary property of the bifurcation curves for a positone problem with cubic nonlinearity {u ''(x)+lambda f(u) = 0, -1 < x <1, u(-1) = u(1) = 0, f(u) = -epsilon u(3) + sigma u(2) + tau u + rho, where lambda > 0 is a bifurcation parameters, epsilon > 0 is an evolution parameter, and sigma, rho > 0, tau >= 0 are constants. In addition, we improve lower and upper bounds of the critical bifurcation values (epsilon) over tilde of the problem.
引用
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页码:639 / 661
页数:23
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