Solvability And Controllability Of Non-Autonomous Impulsive Evolution Equations With Nonlocal Conditions

Evolution equation in abstract spaces is one of important branches in the theory of nonlinear analysis.The researches on the solvability and controllability of initial and boundary value problems of these equations have theoretical significance.In this thesis,based on existing literatures,the existence of mild solutions for a class of non-autonomous impulsive evolution equations with nonlocal conditions is studied.In addition,the controllability of mild solutions for two classes of non-autonomous impulsive evolution equations with nonlocal conditions are investigated.The main results of this paper are as follows:Firstly,under the measure of non-compactness conditions,the existence of mild solutions for non-autonomous impulsive evolution equations with nonlocal conditions is studied in a Banach space by using Sadovskii-Krasnosel’skii-type fixed point theorem.Secondly,without the compactness conditions or Lipschitz conditions on nonlocal term,sufficient conditions for the existence and approximate controllability of non-autonomous impulsive evolution equations with nonlocal conditions are established in a Hilbert space.The discussion is based on Schauder’s fixed point theorem and approximation technique.Finally,by constructing approximating minimizing sequences of functions twice,we investigate the optimal controls for a class of non-autonomous impulsive evolution equations with nonlocal conditions in a Banach space.