The Existence And Application Of Solutions Of Nolinear Impulsive Integro-Differential Equations

In recent years, nonlinear functional analysis is a branch of modern analysis mathematics, it is very important because it can explain a lot of natural phenomena s clearly, so mathematical researchers are devoting their time to it. Among them, the nonlinear problem is at present one of the most active fields that is studied in analysical mathematics. The present thesis mainly discusses the problems for solutions of integral periodic boundary value problems for second order impulsive integro-differential equations with deviating arguments, nonlinear boundary value problems for systems of first order impulsive integro-differential equations with deviating arguments, and fix point theorem is the important tool of researching all kinds of equations.In chapter one, we mainly introduce background, research meaning and current situations of this study, and the main conclusions and motive of this thesis.In chapter two, we discuss the problems for solutions of integral periodic boundary value problems for second order impulsive integro-differential equations with deviating arguments, by using a comparison result and partial method. It generalizes and improves some former corresponding results.In chapter three, we investigate nonlinear boundary value problems for systems of first order impulsive integro-differential equations with deviating arguments by using the cone theory and monotone iterative technique. Our results improve and extend many recent results.In chapter four, according to the fixed point theiry in the functional analysis, we investigate new common fixed point theorems for maps on cone metric spaces. Our results improve and extend some recent results.