Some existence and uniqueness results of a houseflies model with a delay depending on time and state

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