Existence and properties of solutions to differential inclusions

ABSTRACT Master of Science Thesis EXISTENCE AND PROPERTIES OF SOLUTIONS TO DIFFERENTIAL INCLUSIONS SERPİL IZGI Anadolu University Graduate School of Natural and Applied Sciences Mathematics Program Supervisor: Prof. Mahide Küçük 2001, 81 pages In this study, existence of solutions to differential inclusions is searched. Firstly, basic definitions and theorems which are used in other parts are presented. In the second part existence of solutions to Cauchy problem for compact convex val ued differential inclusions is proved. In the third part theorems which connect with closed and compact of solutions set, reachable set and integral funnel for Cauchy problem are proved and a local property of solutions is given. In the final part regularization of differential inclusions with non-convex valued right-hand side and for this type differential inclusions, existence of solutions to Cauchy problem are searched. The last section in this part includes the analysis of the solutions of differential inclusions. It has been proven that, for a point arbitrarily selected out side the integral funnel, there can be at least one solution where the differential inclusion passes through this point and always remains outside the integral fun nel. Keywords: Set- Valued Maps, Lower and Upper Semicontinuity, Differential Inclu sions, Reachable Set, Integral Funnel.