Impulsive delay differential inclusions applied to optimization problems

TL;DR

This paper investigates impulsive delay differential inclusions with infinite delay in Banach spaces, establishing existence of solutions and applying results to optimization and population dynamics models.

Contribution

It introduces a framework for impulsive differential inclusions with infinite delay and proves solution existence using fixed point methods, extending previous models.

Findings

Existence of mild solutions for the class of impulsive delay differential inclusions.

Solution set is compact under certain conditions.

Applications demonstrated in optimization and population dynamics models.

Abstract

We study a class of semilinear impulsive differential inclusions with infinite delay in Banach spaces. The model incorporates multivalued nonlinearities, impulsive effects, and infinite memory, allowing for the description of systems influenced by long-lasting past states and sudden changes. We prove the existence of mild solutions and the compactness of the solution set using fixed point methods and measures of noncompactness. The theoretical results are applied to an abstract optimization problem and to a population dynamics model.