Banach空间变系数的一阶非线性微分方程的正周期解  

Positive periodic solutions for nonlinear first order differential equations with changing of coefficents in Banach spaces

作　　者：李小龙 LI Xiaolong(College of Mathematics and Statistics, Longdong University, Qingyang 745000, Chin)

机构地区：[1]陇东学院数学与统计学院,甘肃庆阳745000

出　　处：《延边大学学报（自然科学版）》2018年第1期14-18,共5页Journal of Yanbian University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11561038);甘肃省高等学校科研项目(2016B-103)

摘　　要：讨论了Banach空间E中变系数的一阶非线性常微分方程u′(t)+a(t)u(t)=f(t,u(t)),t∈R正ω-周期解的存在性,其中a(t)∈C(R,(0,+∞)),f∶R×P→P连续,P为E中的正元锥.利用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,所得结果改进和推广了文献[5-8]中的相关结论.The existence of positive ω -periodic solutions for first order differential equations u＇（t）＋a（t）u（t）=f（t,u（t））, t∈R in Banach spaces E was discussed, where a（t）∈C（R,（0,＋∞））, f：R×P→P is continuous, and P is the cone of positive elements in E. An existence result of positive ω -periodic solutions was obtained by using the fixed point index theory of condensing mapping. The results extended and improved the relevant conclusion in the literature [5-8].

关 键 词：闭凸锥 周期解 凝聚映射 不动点指数 

分 类 号：O175.15[理学—数学]