Positive Periodic Solutions for a First-Order Nonlinear Neutral Differential Equation with Impulses on Time Scales

Abstract

In this article, we discuss the existence of a positive periodic solution for a first-order nonlinear neutral differential equation with impulses on time scales. Based on the Leggett–Williams fixed-point theorem and Krasnoselskii’s fixed-point theorem, some sufficient conditions are established for the existence of positive periodic solution. An example is given to show the feasibility and application of the obtained results. Since periodic solutions are solutions with symmetry characteristics, the existence conditions for periodic solutions also imply symmetry.