The logistic equation in the context of Stieltjes differential and integral equations

Abstract

In this paper, we introduce logistic equations with Stieltjes derivatives and provide explicit solution formulas. As an application, we present a population model which involves intraspecific competition, periods of hibernation, as well as seasonal reproductive cycles. We also deal with various forms of Stieltjes integral equations, and find the corresponding logistic equations. We show that our work extends earlier results for dynamic equations on time scales, which served as an inspiration for this paper.