We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.
In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order .
In this paper we obtain existence conditions and an explicit closed form expression of the general solution of twopoint boundary value problems for coupled systems of second order differential equations with a singularity of the first kind. The approach is algebraic and is based on a matrix representation of the system as a second order Euler matrix differential equation that avoids the increase of the problem dimension derived from the standard reduction of the order method.
In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.
We present some existence results for boundary value problems for first order multivalued differential systems. Our approach is based on topological transversality arguments, fixed point theorems and differential inequalities.
This paper is concerned with the existence of solutions for some class of functional integrodifferential equations via Leray-Schauder Alternative. These equations arised in the study of second order boundary value problems for functional differential equations with nonlinear boundary conditions.
In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered.
Let be a Carath’eodory’s function. Let , with , and be two real sequences. In this paper, the family of boundary value problems is considered. It is proved that these boundary value problems admit at least a solution for each , where is a suitable integer. Some particular cases, obtained by specializing the sequence , are pointed out. Similar results are also proved for the Picard problem.