Document Type : Research Paper

Authors

• Lynda Mezghiche
• Rabah Khemis
• Ahleme Bouakkaz

Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of 20 August 1955, Skikda, Algeria

Abstract

This work elucidates the sufficient conditions for establishing some existence and uniqueness results for a Musca Domestica model that is governed by a first-order nonlinear differential equation with iterative terms resulting from a time and state-dependent delay. The existence of at least one positive periodic solution is proved by using Schauder's fixed point theorem with the help of some properties of an obtained Green's function. Furthermore, under an additional condition, the Banach contraction principle is applied to guarantee the existence, uniqueness and stability of solutions. Finally, the validity of our main findings is demonstrated by two examples. Our findings are completely new and generalize previous ones to some degree.

Keywords

• Delay differential equation
• fixed point theorem
• Green's function
• periodic solution
• positive solution