Impulsive delay differential inclusions applied to optimization problems

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.