The Solutions Of Nolinear Impulsive Integro-Differential Equations

Nonlinear functional analysis is an important branch of modern analysis mathematics. It can explain a lot of natural phenomena clearly, so more and more mathematical researchers are devoting their time to it. Among them, the nonlinear problem comes from a lot of branches of applied mathematics and physics, it 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 boundary value problems with causal operators , integral boundary value problems for first order impulsive integro-differential equations of mixed type and nonlinear boundary value problems for first order impulsive integro-differential equations of mixed type.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 existence of solutions of f integral boundary value problems with causal operators, by using a comparison result and partial method. It generalizes and improves some former corresponding results.In chapter three, by using the cone theory and monotone iterative technique, we investigate the existence of extremal solutions and unique solutions of integral boundary value problems for first order impulsive integro-differential equations of mixed type. Our results improve and extend many recent results.In chapter four, by using lower and upper solutions, we investigate the existence of unique solution of nonlinear boundary value problems for first order impulsive integro-differential equations of mixed type. Our results improve and extend some recent results.