Nonlinear Singular Differential Equations (group) Existence Of Positive Solutions Of Boundary Value Problems And Multiple Solutions,

Nonlincar functional analysis is an important branch in modern analytical mathematics, along with the development of science and technology, nonlinear functional analysis has become an important tool of study the nonlinear problem of mathematics, physics, aerospace technology and biological technology. The boundary value problem of nonlinear differential equation stems from the applied mathematics, the physics, the cybernetics and each kind of application discipline. The nonlocal boundary value problem and periodic boundary value problem of singular nonlinear differential equation, as well as the boundary value problem of impulsive differential equation has attracted much attention of many scholars. So they become a very important domain of differential equation research at present. In this paper, we use the cone theory, the fixed point theory, Leggett-Williams fixed point theorem, non-linear alternative and the the fixed point index theory to study the existence of multiple positive solutions of singular nonlinear differential equation and impulsive differential equation.The thesis is divided into three chapters according to contents.In chapter 1, by using Leggett-Williams fixed point theorems and making a substitution, we considered the existence of multiple solutions for nonlocal boundaryvalue problem of nonlinear second-order singular semi-positone differential equations:We proved the existence of three positive solutions for boundary value problem (1.1.1) with the nonlinear term is semi-positone. The main reult of this paper generalize and improve the results in [5,6].In chapter 2, by using the non-linear alternative of Leray-Schauder type and Schauder fixed point theorem, we investigated the existence of positive solutions for singular semi-positone non-linear third-order differential equations:We also give the applications of the main results.In chapter 3, by using fixed point index theorem, we considered the existence of multiple positive solutions for a class of second-order impulsive differential equations with integral boundary conditions and one-dimensional p-Laplacian:...