Existence And Convergence Of Solutions For Functional Differential Equations

In this paper, we study the existence and convergence of solution sequences for the peri-odic boundary value problem for functional differential equations and the existence of extremesolutions for the impulsive integro-differential equation of mixed type with impulsive integralconditions. At last, we develop a new impulsive integral condition and discuss the existence andconvergence of solution sequences for a nonlinear ordinary differential equation with the newimpulsive integral condition.The main tool is the method of upper and lower solutions coupledwith the monotone iterative technique and the quasilinearization method.The contents of this paper are as follows:In chapter1, we study the problem background knowledge and its development status anda brief description of the main work and subject sources.In Chapter2, we firstly obtain the existence and convergence of solution sequences for theperiodic boundary value problem of functional differential equations by the monotone iterativetechnique and the method of quasilinearization.In Chapter3, we discuss the existence of extreme solutions for the impulsive integro-differential equation of mixed type with impulsive integral conditions.In Chapter4, we discuss the existence and convergence of solution sequences for a non-linear ordinary differential equation with the new impulsive integral condition.