无穷时滞泛函微分方程正周期解的存在性与多解性

应用非线性泛函分析理论中的不动点指数定理、算子理论与锥理论,讨论了一类泛函微分方程的正周期解问题,与已往文献结果相比,研究结果不但获得了该类方程正周期解的存在性定理,而且在此基础上获得了该类方程正周期解的多解性定理.最后,利用Hematcpoiesis模型说明了所得结论在研究具有无穷时滞泛函微分方程正周期解的存在性与多解性问题中的有效性.

Existence and Multiplicity of Positive Periodic Solutions to Functional Differential Equations with Infinite Delay

A class of positive periodic functional differential equations are investigated by nonlinear functional analysis including the fixed point index theorem,operator theorem and cone theory.Compared with the earlier works as shown in reference,both the existence and multiplicity theorems of such functional differential equations with infinite delay are obtained.An example is given to illustrate the conclusion drawn,where the effectiveness of the existence and multiplicity theorems is further proved by Hematcpoiesis model for the positive periodic solutions to the functional differential equations with infinite delay.