A semi-fredholm approach to periodic dynamics in linear reaction-diffusion models with multi-delays

Abstract

This study explores the existence of periodic solutions in linear reaction-diffusion systems with distributed multi-delays, inspired by models arising from the heat equation and population dynamics. We discuss the Massera's problem to this class of equations. Especially, by merging semi-Fredholm operator perturbation techniques with fixed-point methods, we establish sufficient conditions for the existence of periodic solutions, even without assuming compactness of the semigroup generated by the linear part of the equation. As a concrete application, we investigate selected reaction-diffusion models and complement the theoretical results with numerical simulations for illustration.