Existence Of Solutions For Boundary Value Problems Of Second Order Ordinary Differential Equations In Banach Spaces

In this thesis,we study the existence of solution for two-point boundary value problems and periodic boundary value problem of second ordinary differential equation in banach spaces.By doing precise computation of spectral radius of linear operator of linear equation,using measure of noncompactness and topological degree of condensing mapping,upper and lower solution method and monotone iteration technique.Under the copactness condition,we show some existence and unique of two-point boundary value problem under weaker condition.The main results of this paper improve and extend the result of [9,10,11,12].For periodic boundary value problem,By applying precise estimation of solution operator norm of linear periodic and Krasnoselskii s type fixed point theorem of condensing mapping in cones.we show the existence of periodic boundary value problem and obtain some new existence results of positive a> - periodic solution.The main characters of these results are that we delete the condition of nonlinear term s ordinal increasing.The main tools of the thesis are partial order theory,Kuratowski measure of noncompactness and fixed point theorem of condensing mapping in cones and topological degree of condensing mapping...