The Existence Of Solutions For Second-order Differential Equations With Integral Boundary Value Conditions

This paper is concerned with the existence for solutions of second-order boundary value problems. The main results are obtained by using the fixed index theory and cone theory. Some relevant results are extended and improved. The thesis is divided into four chapters:In chapter1, we introduce the background for the discussed problems of this thesis briefly, and we state the main results concretely.In chapter2, we discuss the following second-order differential equation with inte-gral boundary conditionsBy using Banach contraction principle and the fixed point index theory, we study the existence-uniqueness of solutions and the existence of positive solutions.As applica-tion, we give an example.In the chapter3, we study the existence of solutions for second-order impulsive integro-differential equationBy applying M onch fixed point theorem, we obtain the existence of solutions about this problems. This result extends some of the prerious literature.In chapter4, we focus on the existence of solutions for second-order impulsive integro-differential equationBy using M onch fixed theorem, we extend some of the existing conclusions.