Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption

Abstract

Abstract In this paper, we investigate the existence of mild solutions as well as optimal controls for non-autonomous impulsive evolution equations with nonlocal conditions. Using the Schauder’s fixed-point theorem as well as the theory of evolution family, we prove the existence of mild solutions for the concerned problem. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control result is derived by setting up minimizing sequences twice. An example is given of the application of the results.

Keywords

• Impulsive evolution equation
• Optimal controls
• Nonlocal conditions
• Resolvent operator
• Schauder’s fixed point theorem