非线性含参系统无穷多正周期解的存在性  

Existence of Infinite Positive Periodic Solutionsfor Nonlinear Systems with Parameters

作　　者：杨伟 YANG Wei(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,兰州730070

出　　处：《吉林大学学报（理学版）》2021年第5期1025-1030,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061064).

摘　　要：用Krasnoselskii不动点定理,讨论非线性含参系统u′(t)+a(t)u(t)-b(t)v(t)=λf(t,u(t),v(t)),0≤t≤1,v′(t)+b(t)v(t)+a(t)u(t)=λg(t,u(t),v(t)),0≤t≤1,u(0)=u(1),v(0)=v(1)无穷多正周期解的存在性,得到了其无穷多个正周期解,其中λ是一个正参数,a,b:[0,1]→[0,∞)是连续函数且在[0,1]的任意子区间上不恒为0,f,g:[0,1]×[0,∞)×[0,∞)→[0,∞)是连续函数.By using the Krasnoselskii fixed-point theorem,the author discuss existence of infinite positive periodic solutions for nonlinear systems with parameters u′(t)+a(t)u(t)-b(t)v(t)=λf(t,u(t),v(t)),0≤t≤1,v′(t)+b(t)v(t)+a(t)u(t)=λg(t,u(t),v(t)),0≤t≤1,u(0)=u(1),v(0)=v(1),and obtain infinite positive periodic solutions,whereλis a positive parameter,a,b:[0,1]→[0,∞)are continuous function and are not always 0 on any subinterval of[0,1],f,g:[0,1]×[0,∞)×[0,∞)→[0,∞)are continuous function.

关 键 词：多解 非线性 含参系统 周期解 锥上不动点定理 

分 类 号：O175.8[理学—数学]