scholarly journals Positive μ-pseudo almost periodic solutions for some nonlinear infinite delay integral equations arising in epidemiology using Hilbert’s projective metric

2018 ◽  
Vol 5 (1) ◽  
pp. 89-101
Author(s):  
Khalil Ezzinbi ◽  
Mohamed Ziat
Keyword(s):  
Periodic Solutions ◽  
Integral Equations ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solutions ◽  
Projective Metric ◽  
Pseudo Almost Periodic

Abstract The purpose of this work is to give sufficient conditions which guarantee the existence and the uniqueness of positive μ-pseudo almost periodic solutions for the nonlinear infinite delay integral equation . We improve the original work of [H. S. Ding, Y. Y. Chen and G. M. N’Guérékata, Existence of positive pseudo almost periodic solutions to a class of neutral integral equations, Nonlinear Analysis. Theorey, Methods and Applications 74 (2011) 7356-7364] by dropping the hypotheses of monotonicity on the functions f and h. The main results are proved by using the Hilbert’s projective metric combined with the contraction mapping principle. Our results can deal with some cases to which many results are not applicable. An example is provided to illustrate the main results of this work.

scholarly journals Global Exponential Stability of Positive Pseudo-Almost-Periodic Solutions for a Model of Hematopoiesis

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Junxia Meng
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Multiple Time ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solution ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

This paper presents a new generalized model of hematopoiesis with multiple time-varying delays. The main purpose of this paper is to study the existence and the global exponential stability of the positive pseudo almost periodic solutions, which are more general and complicated than periodic and almost periodic solutions. Under suitable assumptions, and by using fixed point theorem, sufficient conditions are given to ensure that all solutions of this model converge exponentially to the positive pseudo almost periodic solution for the considered model. These results improve and extend some known relevant results.

scholarly journals Existence and control of weighted pseudo almost periodic solutions for abstract nonlinear vibration systems

2018 ◽  
Vol 38 (2) ◽  
pp. 765-773
Author(s):  
Yingxin Guo ◽  
Fei Wang ◽  
Luyao Xin
Keyword(s):  
Nonlinear Vibration ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solutions ◽  
Precise Bound ◽  
The Stability ◽  
Pseudo Almost Periodic ◽  
And Control

In many vibration problems, it is very important to know precisely the bounds of the stability/instability frequencies and the associated amplitude ranges. This paper investigates the solvability and control of some weighted pseudo almost periodic solutions of abstract nonlinear vibration differential systems. Some sufficient conditions for the solvability and exponential stability of these systems are obtained. Moreover, the precise bound of Lyapunov exponents is estimated.

scholarly journals Pseudo Almost Periodic Solutions for HCNNs with Time-Varying Leakage Delays

2015 ◽  
Vol 1 (1) ◽  
pp. 51-69 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Periodic Solutions ◽  
Exponential Dichotomy ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Pseudo Almost Periodic Solutions ◽  
The Fixed Point Theorem ◽  
Pseudo Almost Periodic

Abstract In this paper, we consider a class of high-order cellular neural networks (HCNNs) model with time-varying delays in the leakage terms. We give some sufficient conditions which guarantee the exponential stability of pseudo almost periodic solutions for the model. The obtained results complement with some recent ones in the literature.The technique of proof involves the exponential dichotomy theory and the fixed point theorem. An illustrative example is given with an application.

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