Research On Periodic Solutions And Almost Periodic Solutions For Differential Equations With Delays

This dissertation investigates the existences of periodic solution and almost period-ic solution for several kinds of functional differential equations.By using the coincidence degree theory due to Mawhin we study the existence of periodic solutions for a class of nonlinear second order differential equations with delays.We consider the existence of pos-itive solutions for boundary value problem of nonlinear fractional differential equations by using Krasnoselkiis fixed-point theory and Leggett-Williams fixed-point theory.Some suf-ficient condition to the existence and exponential convergence of almost periodic solutions of functional differential equations are obtained by utilizing exponential dichotomy and fixed-point theory.The thesis is organized as follows:The Chapter1introduces the historical backgorund of the research questions mainly. Secondly, it introduces the reason for choosing the topic.In Chapter2,by using the coincidence degree theory due to Mawhin,the existence of periodic solutions for a class of nonlinear second order differential equations with delays is studied.Sufficient conditions for the existence of multiple positive solutions are established.In Chapter3,we study the existence and exponential convergence of almost periodic solutions of generalized functional differential equations by utilizing contraction mapping principle and exponential dichotomy.In Chapter4,by using Krasnoselkiis fixed-point theory and Leggett-Williams fixed-point theory we study the existence of positive solutions for boundary value problem of nonlinear fractional differential equations.Sufficient conditions for the existence of multiple positive solutions are established under weaker conditions.Some recent results are extend and improved.