Almost periodic solutions for an impulsive delay Nicholson’s blowflies model

AbstractBy means of the contraction mapping principle and Gronwall–Bellman’s inequality, we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay Nicholson’s blowflies model. The main results are illustrated by an example

Perron-Type Criterion for Linear Difference Equations with Distributed Delay

It is shown that if a linear difference equation with distributed delay of the form Δx(n) , n ≥ 1, satisfies a Perron condition then its trivial solution is uniformly asymptotically stable

Almost periodic solutions of impulsive integro‐differential neural networks

In this paper, sufficient conditions are established for the existence of almost periodic solutions for system of impulsive integro‐differential neural networks. Our approach is based on the estimation of the Cauchy matrix of linear impulsive differential equations. We shall employ the contraction mapping principle as well as Gronwall‐Bellman's inequality to prove our main result. The research of Gani Tr. Stamov is partially supported by the Grand 100ni087–16 from Technical University–Sofia First published online: 10 Feb 201

Existence of periodic solutions for Rayleigh equations with state-dependent delay

We establish sufficient conditions for the existence of periodic solutions for a Rayleigh-type equation with state-dependent delay. Our approach is based on the continuation theorem in degree theory, and some analysis techniques. An example illustrates that our approach to this problem is new

The -Fractional Analogue for Gronwall-Type Inequality

We utilize -fractional Caputo initial value problems of order to derive a -analogue for Gronwall-type inequality. Some particular cases are derived where -Mittag-Leffler functions and -exponential type functions are used. An example is given to illustrate the validity of the derived inequality