Periodicity and positivity of solutions for first-order nonlinear neutral differential equations with iterative terms and impulsive effects

In the present paper, sufficient conditions for the existence of bounded positive periodic solutions are established for a class of nonlinear neutral differential equations with iterative source term and nonlinear impulses. The form including an impulsive term of the equations in this paper is rather general and incorporates as special cases various problems which have been studied extensively in the literature. Transforming the considered equation to an equivalent integral equation, we prove the existence of positive periodic solutions using a Krasnoselskii fixed point theorem for the sum of a contraction and a compact mapping. Finally, we present an example to illustrate the effectiveness of our results.