Existence Of Solutions Of Equation Boundary Value Problems Of Nonlinear Singular Differential Equations And Pulse

Nonlinear functional analysis as an important research subject which developed on mathe-matics and natural science in recent years is an effective theory in solving nonlinear problems in such fields as math, biology, physics and engineering mechanics.etc. The main research meth-ods of nonlinear problems are upper and lower solution method, partial order method, variations method, topology degree method, coincidence degree method and so on. The major issues to the research are the existence of solutions, multiple existence and number of solutions, differences of solution, and iteration of solution for nonlinear operator equations as well as the application for differential-integral equation and partial differential equation. Therefore, the study on nonlin-ear singular differential equation and impulsive equation boundary value has become a new topic which is very meaningful and interesting.Based on semi-order space theory about nonlinear analysis and through the use of nonlinear functional analysis methods, this article studies the existence of solution of fourth order differen-tial equation and second order impulsive equation boundary value problem in Banach space. By deep study, we obtained some new results and also provided a different approach for the different of nonlinear singular points and boundary conditions.This paper is divided into the following five chapters. The first chapter is on the introduction of the historical background and current development of nonlinear analysis. Besides, it introduces the topic of this paper generally. The second chapter is about the concepts, lemmas and symbols used in this paper. In the third chapter, according to the study, when the nonlinear term is in the event of t=0, t=1 and x=0, the fourth-order two-point boundary value problem got the existence of solution. In the fourth chapter, by using the cone expansion and compression fixed point theory, the author focuses on whether the solution of the four-order three point boundary value problem exists or not under the situation of parameter boundary values. In the last chapter, Chapter 5, the composer studies on impulse equation. With the help of compressive fixed point theory, a new theorem of existence of solutions for impulse equation is obtained.