The Presence Of Several Types Of Nonlinear Equations And Their Applications

Nonlinear functional analysis is an important branch of modern analysis mathematics, because it can explain all kinds of natural phenomenon, more and more mathematicans are spending their time on it. Among them, the nonlinear impulsive problems and singular boundary problems arise from a lot of branches of applied mathematics and physics, which are at present active fields in analysis mathematics. The paper is divided into four chapters according to the contents.In the first chapter, we give the preface.In the first section of Chapter Two, by using the Monch fixed point theorem and a comparison result, we shall study the existence theorems of solutions of intial value problem for the first order nonlinear impulsive integro-differential equations :In the second section of Chapter Two, we study the existence of a unique solution of the following equation under the hypothesis that the equation does not satisfy any compactness-type conditions and has only an upper (or a lower)solution:In the third chapter, we exploit a new comparison result and the Monch fixed point theorem to prove the existence theorem of global solutions for two-point boundary value problems of second order impulsive integro-differential equations in Banach spaces:...