Class Of Nonlinear Differential Equations Boundary Value Problem, Positive Solution,

In this paper, we use the cone theory, the fixed point theory, fixed point index theory as well as the methods of lower and upper solution, to study the solutions for kinds of integral boundary value problems and impulsive differential equation, and we apply the main results to the boundary value problem for the integral differential equations and impulsive differential equations.The thesis is divided into four chapters according to contents.The first chapter chiefly narrates the background of the nonlinear analysis, the research subject and the innovation of this paper.In chapter 2, using the methods of lower and upper solution, and the fixed point theorem, we are concerned with the existence and uniqueness of positive solution for the following integral boundary value problem The nonlinearity f(t,u)∈C((0,1) x (0,+∞), [0,+∞)) may be singular at t= 0, t= 1 and u= 0, and f(t, u) is nonincreasing on u, a∈C([0,1], [0,+∞)) andIn chapter 3, by Leggett-Williams fixed point theorem and Krasnoselskii's fixed point theorem, we investigate the existence of multiple positive solutions for the singular second-order integral boundary value problems h(t)∈C((0,1),(0,+∞)),f (t,u)∈C([0,1]×[0,+∞),[0,+∞)), a(s)∈C([0,1], [0,+∞)) and h(t) may be singular at t= 0,t= 1.In chapter 4, by fixed point index theorem and the properties of the Green function, we investigate the existence of positive solutions for the impulsive dif- ferential equations boundary value problems are right limit (left limit) respectively for the u'(t) and u(t) at t= tk.