Optimal control for a class of strongly nonlinear impulsive equations in Banach spaces

In this paper, we consider the optimal control problem of system governed by a class of strongly nonlinear impulsive evolution equations. Based on the existence of strongly nonlinear impulsive evolution equations, which contain nonlinear monotone operators and nonmonotone perturbations, we prove the existence of optimal controls for the general Lagrange problem. The necessary conditions for optimality are also presented.