On the Properties of the Set Solutions of a Class of Paratingent Equation with Delay
Lotfi Boudjenah *
Department of Information Sciences, University of Oran, BP 248, Senia Zerbani Oran 31106, Algeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper we will study the main properties of the set solutions of the paratingent equation (type differential inclusion) with delay of the form: (Ptx)(t) ⊂ F([x]t) for t ≥ 0 with the initial condition: x(t) = ξ(t) for t ≤ 0. We will be interested particularly in the topological properties of the set solutions and the continuous dependence on initial conditions of the set solutions.
Keywords: Attainable set, compact, continuous dependence, delay, differential inclusion, emission, paratingent, set solutions