Existence And Stability Of Impulsive Differential Equations

Impulsive differential equations can be successfully used for mathematical simulation in theoretical physics, chemistry, biotechnology,medicine, population dynamics, optimal control, and in other processes and phenomena in science and technology. The existence theory of impulsive differential equations has been developed by a large number of mathematicians,and those studies have attracted much attention. They have been successful in different approaches based on comparison technique and Lyapunov method.In this paper include:Successfully using iterative analysis method get some pulsive delay differential equations and sufficient condition of the existence,uniqueness and stablility of their solutions.The second chapter introduced Picards existence and uniqueness theorems in ordinary differential equations which prove the existence and uniqueness of solutions and this paper used to study various types of differential equations existence and stability of the iterative analysis method.The third chapter introduced Picards existence and uniqueness theorems were extended to the pulse of ordinary differential equations and the ordinary differential equations system, and also get its full conditions of stability and the time decay estimates.The fourth chapter,iterative analysis method is applied to a more common, which also have a very broad application of a class of neutral delay differential equations, get its existence, uniqueness, stability of solution and the time decay estimates.The fifth Chapter, a class of partial differential equations with impulsives is been discussed in its solution existence, uniqueness, stability, and the time decay estimates with the iterative analysis methods.On the last part, further study were summarized and prospects.Through this discussion, we can clearly understand: research by the delay or pulsive problems and the existence of solutions with the conclusions of stability and pulsive delay variable conditions are inseparable.