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有序Banach空间中常微分方程正周期解的存在性
引用本文:李小龙.有序Banach空间中常微分方程正周期解的存在性[J].系统科学与数学,2012,32(2):190-196.
作者姓名:李小龙
作者单位:陇东学院数学与统计学院,庆阳,745000
基金项目:陇东学院青年科技创新项目
摘    要:讨论了有序Banach空间E中的非线性常微分方程:u′(t)+Mu(t)=f(t,u(t)),(?)t∈R正ω-周期解的存在性,其中f:R×P→P连续,P为E中的正元锥.通过新的非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正ω-周期解的存在性结果.

关 键 词:闭凸锥  正ω-周期解  凝聚映射  不动点指数

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR ORDER DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACES
LI Xiaolong.EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR ORDER DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACES[J].Journal of Systems Science and Mathematical Sciences,2012,32(2):190-196.
Authors:LI Xiaolong
Institution:LI Xiaolong (School of Mathematics and Statistics,Longdong University,Qingyang 745000)
Abstract:The existence of positiveω-periodic solutions for order differential equations u’(t)+Mu(t)=f(t,u(t)),(?)t∈R in an ordered Banach spaces E is discussed,where f:R×P→P is continuous,and P is the cone of positive elements in E.An existence result of positiveω-periodic solutions is obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.
Keywords:Closed convex cone  positive periodic solution  condensing mapping  fixed point index
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