3 rd INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES, İstanbul, Turkey, 4 - 08 September 2019, pp.40
In this paper, for a problem second order evolution differential inclusions with phase constraints the op-
timality conditions are derived. Necessary and sufficient conditions ensuring the existence of a solution to
the problems for evolution differential inclusions of second order have been studied in recent years. There
are limited number of articles devoted to the optimization problem of second order evolution differential in-
clusions with phase constraints. We apply optimality conditions to problems with geometric constraints and
conditions for second order discrete inclusions are proved. We use Locally Dual Mapping definition to derive
necessary and sufficient conditions for the optimality of the discrete approximation problem. Passing to the
limit, sufficient conditions to the optimal problem are established.
Keywords: Second order differential inclusion, Locally dual mapping, evolution.