Research On Existence Of Solutions For A Class Of Second Order Impulsive Differential Equations

In real life, Many systems and movements can be described by Ordinary Differential Equations. But, It represents a more natural framework for mathematical modeling of many real world phenomena than ordinary differential equations. It shows some processes which distinguished at certain instants that their state is subjected to a sudden change, for example, in population dynamics, physics, ecology, biological systems, etc. Essentially, impulsive differential equations and order differential equations have great difference. In order to reveal the impacts and effects which are generated by impulse, this paper mainly investigates the existence of solution for a class of second order impulsive differential equations. In the second chapter, we investigate the nonexistence of solutions for a class of second order impulsive differential equations at first, and then we consider the existence of positive solutions and multiple positive solutions of second order impulsive boundary value problems by constructing the appropriate homotopic operator and applying the theory of fixed point index in cones. In the third chapter, we investigate the existence of solution to the control system. It can be seen that the existence of solution for differential equations may be changed completely because of impulse.