Study Of Positive Solutions On Boundary Value Problems For Second Order Ordinary Differential Equations With P-Laplacian

Differential equations have a profound and vivid actual background. They arise from the development of Production and science technology,until now they becomes to Powerful instrument to analyze and solve Problems in the modern science and technology. they play an important role in the field of economic and financial insurance, the analysis of the structure of the number of biological species, and the control and prevention of diseases and insect pests and so on. The differential equations have provided an extremely apropriate mathematical model for the research such as above realistic question developing process, become an extremely active research direction for their importance.It's very important to research on the existence of positive solutions of boundary value problems for differential equations, because you can not begin the next step of work for seeking the numerical solutions and applying into Practice, such as inspection, control and Prediction of the Practical Problems, unless we make clear whether and how many solutions exist. Therefore, the study to the existence of solutions of boundary value Problems, especially the existence of Positive solutions, by means of the methods of nonlinear functional analysis arises recent decades years, has greatly attracted many mathematics workers' attention.This dissertation discusses mainly three major boundary value Problems of the existence of solutions for nonlinear ordinary differential equations and some nonlinear equation systems with p-laplacian using fixed Point theorem on the basis of reading a lot of references. The paper discusses three Problems as follows:Firstly, we study the existence of symmetric Positive solutions for some p-laplacian boundary value problems with dependence on the first order derivative, turn the differential equations to integral equations, by using Avery-Peterson fixed Point theorem in cone we get the sufficient conditions for the existence of at least there fixed point of integral operator which is the solutions to the Problem.Secondly, we discuss a class of one-dimensional p-Laplace operator boundary value Problems with dependence on both the first order derivative and the second order derivative, by variable substitution we turn the Problems to general equation; The nonlinear f conclude the Part less than 0, this brings us more difficulties in solving the Problems, we turn the Part less than 0 to non-negative through appropriate treatment , then using fixed point index theorem, we obtain sufficient conditions for the existence of positive solution of the above boundary value problem.Thirdly, we discuss the existence of positive solutions to boundary value Problems for systems of nonlinear second order differential equations with p-laplacian, by applying Avery-peterson fixed point theorem in cone to get the sufficient conditions for the existence of at least there solutions to the problem. Some new conclusions are obtained.Finally,we discuss the existence of at least one positive solutions for second order m-point boundary value Problems with dependence on the first order derivative, by applying a new fixed Point theorem in cone to get the sufficient conditions for the existence of at least one solution to the problem.