带参数的一阶周期边值问题正解的全局结构  

Global structure of positive solutions for first-order periodic boundary value problem with parameter

作　　者：王娇 祝岩 WANG Jiao;ZHU Yan(College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

机构地区：[1]西北师范大学数学与统计学院

出　　处：《四川大学学报（自然科学版）》2019年第3期413-418,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11671322);国家自然科学基金天元基金(11626061)

摘　　要：本文运用Dancer全局分歧定理研究了带参数的一阶周期边值问题{u′+a(t)u=rf(u),t∈(0,1),u(0)=u(1)正解的全局结构,获得了正解存在的最优区间.其中r为正参数,f∈C(R,R),a∈C([0,1],[0,∞)),且a(t)在[0,1]的任意子区间内不恒为0.In this paper, we use Dancer’s global bifurcation theorem to study the global structure of positive solutions for the following first-order periodic boundary value problem with parameter:{u′+a(t)u=rf(u),t∈(0,1),u(0)=u(1) where r is a positive parameter, f∈C(R,R),a∈C([0,1],[0,∞)), and a(t) is not identically equal to zero on any subinterval of [0,1]. We obtain the optimal interval for the existence of positive solutions.

关 键 词：周期边值问题 正解 Dancer分歧定理 

分 类 号：O175.8[理学—数学]