Existence of positive periodic solutions for first-order nonlinear differential equations with multiple time-varying delays

Abstract

Abstract This study elucidates the sufficient conditions for the first-order nonlinear differential equations with periodic coefficients and time-varying delays to have positive periodic solutions. Our results are proved using the Krasnosel’skii fixed point theorem. In this article, we have identified two sets Δ \Delta and ∇ \nabla and proved that at least one positive periodic solution exists in the interval between the point belonging to Δ \Delta and the point belonging to ∇ \nabla . We propose simple conditions that guarantee the existence of sets Δ \Delta and ∇ \nabla . In addition, we obtain the necessary conditions for the existence of positive periodic solutions of the first-order nonlinear differential equations when the periodic coefficients satisfy certain conditions. Finally, examples and numerical simulations are used to illustrate the validity of our results.