Roummani Bahya, Johnny Henderson, Abdeghani Ouahab

Existence and Solution Sets for Systems of Impulsive Differential Inclusions

abstract:
In this paper, we consider the existence of solutions and some properties of the set of solutions, as well as the solution operator for a system of differential inclusions with impulse effects. For the Cauchy problem, under various assumptions on the nonlinear term, we present several existence results. We appeal to some fixed point theorems in vector metric spaces. Finally, we prove some characterizing geometric properties about the structure of the solution set such as $AR,$ $R_\delta$, contractibility and acyclicity, with these properties corresponding to Aronszajn-Browder-Gupta type results.

Mathematics Subject Classification: 34A37, 34A60, 34K30, 34K45

Key words and phrases: System of differential inclusions, impulsive, fixed point, existence, vector metric space, $R_{\delta}$-set, acyclic, matrix