The Extremal Solutions Of Initial Value Problem For Second Order Nonlinear Impulsive Integro-Differential Equations In Banach Spaces

The Extremal Solutions of Initial Value Problem For Second Order Nonlinear Impulsive Integro-Differential Equations in Banach SpacesThe theory of nonlinear impulsive differential equations is a new and important brandiof differential equations. Many problems arising in the scientific field lead to mathematical models described by nonlinear impulsive functional differential equations, which made us research this subject seriously. This paper studied the existence of minimal and maximal solutions of initial value problem for nonlinear second order impulsive integro-differential equations in Banach spacesBy using the monotone iterative technique and the comparison results, some existence theorems are obtained. Then, we give some applications to initial value problems for the second order impulsive integro-differential equaations in Banach spaces.