Existence of solutions for dynamic inclusions on time scales via duality

TL;DR

This paper establishes sufficient conditions for the existence of solutions to nabla differential inclusions on time scales, extending the theory of dynamic equations to more general settings with set-valued constraints.

Contribution

It introduces new existence results for solutions of nabla differential inclusions on time scales under specific set-valued constraints, broadening the applicability of dynamic inclusion theory.

Findings

Sufficient conditions for solution existence are derived.

Solutions are shown to stay within the constraint set.

The results unify continuous and discrete cases under a common framework.

Abstract

The problem of existence of solutions to nabla differential equations and nabla differential inclusions on time scales is considered. Under a special form of the set-valued constraint map, sufficient conditions for the existence of at least one solution, that stay in the constraint set, are derived.