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

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].