The Existence Of Solutions For Third-Order Three-Point Boundary Value Problems In Banach Spaces

In this dissertation, by using the fixed point theorem of condensing mapping and the fixed point index theory in cones with the measure of noncompactness, the partial order theory and topological degree of condensing field, the paper discusses the existence of solutions for third-order three-point boundary value problems in Banach spacesThe results of this paper are as follows: 1. With the existence of solutions for corresponding third-order three-point boundary value problems in R, we obtain the existence and uniqueness of the third-order linear differential equation three-point boundary value problems in Banach spaces.2. By the monotone iterative technique in presence of upper and lower solu-tions, In Banach spaces, we get the results of the existence and uniqueness of the third-order three-point boundary value problems.3. Under the measure of noncompactness conditions, by using the Sadovskii fixed point theorem and Leray-Schauder fixed point theorem of condensing mapping, we get the existence of solutions of the nonlinear third-order three-point boundary value problems in Banach spaces.4. By constructing a special cone, applying the Cone expansion and compression fixed point theorem and using the fixed point index theory of condensing mapping in cones, the existence of positive solutions of nonlinear third-order three-point bound-ary value problems in Banach spaces are obtained, respectively.