The Study About Analytic Solutions For Three Classes Of Iterative Functional Differential Equations

It is well known that iterative functional differential equations are a kind of differential equations with deviating argument of the unknown function, and the delay function depends not only on argument of the unknown function, but also state or state derivative, even higher order derivatives. From the 1950s, the study of iterative functional differential equations has received considerable attention by many scholars under the impetus of the application problems in many branches of the natural and social sciences. However, the study of the analytic solutions of iterative functional differential equations has lagged behind, which is because of the emergence of unknown function iteration and the inapplicability of the ordinary differential equations classical existence theorem. Based on the implicit function theorem, this dissertation investigates the existence of analytic solutions on three kinds of iterative functional differential equations.The main work of this dissertation can be generalized as follows:1. The existence of analytic solutions on three kinds of iterative functional differential equations is studied by utilizing the majorant series and Banach fixed point theorem. The method is first to change the iterative functional differential equations into another unknown function without iterates by using the SchrOder transformation, and the analytic solutions of an auxiliary equation is obtained by means of majoring series, then the analytic solutions of iterative functional differential equations are derived.2. The breakthrough of the dissertation is further to weaken the condition. The condition based on the Brjuno one is weaker than the Diophantine condition such that the result is more general.