一阶半正常微分系统周期边值问题正解的存在性  

Existence of positive solutions of periodic BVP for a first-order semi-positive ordinary differential system

作　　者：薄志伟 马如云 BO Zhi-Wei;MA Ru-Yun(School of Mathematics and Statistics,Xidian University,Xi'an 710126,China)

机构地区：[1]西安电子科技大学数学与统计学院,西安710126

出　　处：《四川大学学报（自然科学版）》2023年第5期73-78,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(12061064)。

摘　　要：本文研究了一阶半正常微分系统周期边值问题{u(0)=u(1),v(0)=v(1)-v′(x)+b(x)v(x)=λg(x,u(x)),0<x<1,-u′(x)+a(x)u(x)=λf(x,v(x)),0<x<1,正解的存在性,其中,参数λ>0,函数a,b∈C([0,1],[0,∞))且在[0,1]的任何子区间上不恒为0,f,g∈C([0,1]×R,R),f(x,0)<0,g(x,0)<0.基于拓扑度理论,本文证明:存在λ0>0,使得当0<λ<λ0时该问题至少有一个正解.In this paper,the existence of positive solutions of periodic boundary value problem(BVP)for the first-order ordinary differential system{u(0)=u(1),v(0)=v(1)-v′(x)+b(x)v(x)=λg(x,u(x)),0<x<1,-u′(x)+a(x)u(x)=λf(x,v(x)),0<x<1,is studied,whereλis a positive parameter,a,b∈C([0,1],[0,∞))are functions identically non-vanishing on any subinterval of[0,1],f,g∈C([0,1]×R,R),f(x,0)0,g(x,0)0.Underlying the topological degree theory,it is proved that there existsλ_00 such that the problem has at least one positive solution for 0λλ_(0).

关 键 词：周期边界问题 正解 半正问题 拓扑度理论 

分 类 号：O175.8[理学—数学]