Several Types Of The Differential Equation Boundary Value Problem Solution Existence

In recent years, various nonlinear problems has already aroused people’s widespread interest. Among these problems, the boundary value problems of nonlinear differential equations has already become one of the most interested subjects for researchers no matter in home and aboard. In this thesis, we investigate the existence of solutions for two classes of boundary value problems of nonlinear differential equations by using the fixed point theorem and the fixed point index theory. The thesis is composed of four chapters.Chapter1is preface. The scientific background and the significance of the thesis are illustrated. Boundary value problems occur in various fields of natural science. The existence of solutions for boundary value problems attracts much attention of many famous experts and scholars in differential field. We review the present progress of the existence of solutions boundary value problems for nonlinear differential equations, Some knowledge mentioned in this thesis is also summarized.In chapter2, using the Krasnosel’skii fixed point theorem, we discuss the existence of positive solutions of a class of singular nonlinear third-order boundary value problems. We establish various results on the existence of single and multiple positive solutions to the problem. An example is also given to illustrate some of the main results we obtain.In chapter3, we investigate the existence of positive solutions of a class of boundary value problems for singular nonlinear second-order impulsive differential equations by applying the fixed point index theorem, we give some new criteria to guarantee the existence of positive solutions. Some results are generalized in this thesis, a result of the existence of positive solutions is obtained.In chapter4, we investigate the existence and successive iteration of positive solutions for a class of boundary value problems with p-Laplacian on infinite intervals,and the corresponding iterative schemes for approximating the solutions are also given.In chapter5, we summarize our research work and outlook briefly for this thesis.