Existence Of Solutions For Some Classes Of Integral Boundary Value Problems Of Nonlinear Differential Equations

This thesis investigates the existence of solutions and positive solutions for someclasses of boundary value problems of nonlinear diferential equation, positive solution-s of second-order diferential equations with integral boundary conditions on infiniteintervals, existence of positive solutions for a third-order integral boundary value prob-lems with p-Laplacian, the existence of solution for diferential equations with integralboundary conditions on infinite intervals in Banach spaces. The thesis consists of fourchapters.Chapter l is introduction, the historical background of boundary value problemsof diferential equations and the significance of this thesis are introduced. We reviewthe recent development on boundary value problems of diferential equations and alsointroduce the background and main results of our works.In Chapter2, using the fixed point theorem in cone and some techniques of anal-ysis, we discuss second-order diferential equations with integral boundary conditionson infinite intervals, and obtain the existence of, at least one positive solution.In Chapter3, we studied the existence of positive solutions for the nonlocal bound-ary value problems of a type of nonlinear third order diferential equations with integralboundary conditions. By means of fixed points of cone expansion and compression, theexistence of, at least, one and two positive solutions is obtained.In Chapter4, by using the M¨onch fixed point theorem and the Kuratovski non-compactness measure theory, we investigate the existence of solution for diferentialequations with integral boundary conditions on infinite intervals in Banach spaces,and obtain some new results.