On The Periodic Solutions And Controllability Of Second-order Differential Inclusions With Nonlocal Conditions

Differential inclusion is an important branch of nonlinear analysis, which has close relationships with other branches of mathematics such as differential equation, optimal control and optimization. The existence of periodic solutions and control-lability are basic contents of differential inclusions. The main content of this paper is the property of second-order differential inclusions with nonlocal conditions. Par-ticularly, we give the existence theorems of the periodic solusions for second-order differential inclusions with nonlocal conditions. Moreover we study the controllabil-ity several classes of second-order differential inclusions with nonlocal conditions.First, in this paper the existence theorems of the periodic solusions of a class of intergrodifferential inclusions is studied by fixed point theorem. For convex cases, we establish sufficient conditions for the existence theorems of the periodic solu-sions. Our method is based on the transition from the problems discussed to the fixed point problems of setvalued integral operators. By using Kakutani fixed point theorem, we give the sufficient conditions of the existence theorems of the periodic solusions.Then, in this paper by using Kakutani fixed point theorem, the controllability of second-order differential inclusions with nonlocal conditions are studied. Suffi-cient conditions of the controllability are given. The conclusions extend and improve some previous works.