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Nguyen Diep, Phan Van Tri; Existence and Uniqueness of Solutions to Set-valued Control Integro-differential Equations; Institute of Advanced Scientific Research, Vol. 6, Issue 2 (2014), pp. 58-81 (Journal Paper).

Abstract

In the paper, we present existence, uniqueness and comparison of solutions of set control integro-differential equations (SCIDEs) under the form \\ \indent \hfill $ D_H X\left( t \right) = F\left( {t,X\left( t \right),U(t),\int\limits_{t_0 }^t {G\left( {t,s,X\left( s \right),U(s)} \right)ds} } \right) $ \hfill \indent \\ with some suitable conditions. Where $U(t) \in K_{CC}(\mathbb R^d)$ is different controls, inclusion: admissible control, feedback control and contraction control.

Keywords.  Set-valued differential equations; Set-valued integro-differential equations.