Boundary Value Problem And Periodic Solution For Several Classes Of Differential Equations

This thesis of Master is composed of three chapters,which mainly studied the existence of multiple positive solution on m-point boundary value prombles, solvability of second order m-point boundary value problems with impulses and existence of periodic solutions for differential equation with several delays.In chapter one,the existence criterias for multiple positive solutions for mpoint boundray value problems are obtained by using Krasnoselskii fixed point theorem and Leggett-Williams fixed-point theorem.Chapter two,by Leray-Schauder continuation theorem and the nonlinear alternative of Leray-Schauder type,we study the existence of solutions for impulsive boundary value problems on infinity intervals and initial value problems with singular,and some sufficient conditions be given,the existence of a solution for an m-point boundary value problem with impulses is proved.Our results improve some known results or are new.In the last chapter,by means of coincidence degree theory,the existences of periodic solution for a kind of differential equation with several delays are obtained.