Impulsive Nonlocal Neutral Integro-Differential Equations Controllability results on Time Scales

In this work, we studied the controllability results for neutral differential time-varying equation with impulses on time scales & extend these results into nonlocal controllability of neutral functional integro-differential time-varying equation with impulses on time scales. The solutions are obtained employing standard fixed point theorems

Controllability of a semilinear neutral dynamic equation on time scales with impulses and nonlocal conditions

In this paper we consider a control system governed by a neutral differential equation on time scales with impulses and nonlocal conditions. We obtain conditions under which the system is approximately controllable, on one hand, and on the other hand, the exactly controllable is also proved. Concretely, first of all, we prove the existence of solutions. After that, we prove approximate controllability assuming that the associated linear system on time scales is exactly controllable, and applying a technique developed by Bashirov et al. [8, 9, 10] where we can avoid fixed point theorems. Next, assuming certain conditions on the nonlinear term, we can apply Banach Fixed Point Theorem to prove exact controllability. Finally, we propose an example to illustrate the applicability of our results.Publisher's Versio

Nonnegative solutions for a system of impulsive BVPs with nonlinear nonlocal BCs

We study the existence of nonnegative solutions for a system of impulsive differential equations subject to nonlinear, nonlocal boundary conditions. The system presents a coupling in the differential equation and in the boundary conditions. The main tool that we use is the theory of fixed point index for compact maps

Approximate controllability for some integrodifferential measure driven system with nonlocal conditions

In this work, we focus on a specific category of nonlocal integrodifferential equations. The development of a few new sufficient postulates that guarantee solvability and approxi- mative controllability is described here. We apply the theory of the resolvent operator in the sense of Grimmer, as well as the fixed point strategy and the theory of the Lebesgue-Stieljes integral, in the context of the space of regulated functions. In light of this, the prevalence of our findings is greater than that which is found in the literature. At last, and example is comprised that exhibits the significance of developed theory

Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity

We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex values fail. Based on previously obtained results for periodic problems in the single-valued cases, the existence of solutions is proven. It is also pointed out that the solution set is compact in the uniform convergence topology. In particular, the existence results are obtained for periodic impulsive differential inclusions (with multivalued impulsive maps and finite or possibly countable impulsive moments) without upper semicontinuity assumptions on the right-hand side, and also the existence of solutions is derived for dynamic inclusions on time scales with periodic boundary conditions