We consider the Stackelberg problem for coupled parabolic equations with a finite number of constraints on one of the states. This notion assumes that we have two controls to determine. The first control is supposed to bring the solution of the coupled system subjected to a finite number of constraints at rest at time zero while the second expresses that the states do not move too far from given states. The results are achieved by means of an observability inequality of Carleman adapted to the constraints.

In this paper we study the hierarchic control problem for a linear system of a population dynamics model with unknown birth rate. Using the notion of low regret control and an observability inequality of Carleman type, we show that there exist two controls such that, the first control called follower solves an optimal control problem which consist in bringing the state of the linear system to desired state, and the second one named leader is supposed to lead the population to extinction at final time.

In this paper we study the existence and uniqueness of μ− pseudo almost automorphic mild solutions for two term fractional order differential equations in a Banach space with μ− pseudo almost automorphic forcing terms. The fractional derivative is understood in the sense of Weyl. We use classical tools to obtain our results.

In this work we are concern with Clifford-valued semi-linear delay differential equations in a Banach space. By using the Banach fixed point theorem, we prove the existence and uniqueness of µ−pseudo almost automorphic solution for Clifford-valued semi-linear delay differential equations.