The Existence Of Solutions For Third-order Two-point Boundary Value Problems In Banach Spaces

Based on the monotone iterative technique of upper and lower solutions, fixed point theorem about topological degree and the fixed point index theory in cones, the paper discusses the existence and uniqueness of solutions for the third-order two-point boundary value problems of ordinary differential equation where I=[0,1],f:∈C(I×E×E, E).The results of this paper are as follows:1.By establishing a new comparison principle, combining with the monotone iterative technique in presence of upper and lower solutions, the results of the ex-istence and uniqueness of solutions for the third-order two-point boundary value problems are obtained in order Banach spaces2.Under the measure of noncompactness conditions, some existence results for the third-order two-point boundary value problems are obtained by using measure of noncompactness and fixed point theorem about topological degree.3.Under the measure of noncompactness conditions, by using the fixed Point index theory of condensing mapping, the existence of positive solutions for the third-order two-point boundary value problems are obtained in order Banach spaces...