LI Xiaolong.Positive periodic solutions for nonlinear first order differentialequations with changing of coefficents in Banach spaces[J].Journal of Yanbian University,2018,44(01):14-18.
Banach空间变系数的一阶非线性微分方程的正周期解
- Title:
- Positive periodic solutions for nonlinear first order differential equations with changing of coefficents in Banach spaces
- 分类号:
- O175.15
- 文献标志码:
- A
- 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.
- Abstract:
- 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].
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备注/Memo
收稿日期: 2018-01-11
作者简介: 李小龙(1976—),男,副教授,研究方向为抽象微分方程及其应用.
基金项目: 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)