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By using some analytical techniques, modified inequalities and Mawhin's continuation theorem of coincidence degree theory, some sufficient conditions for the existence of at least one positive almost periodic solution of a kind of fishing model with delay are obtained. Further, the global attractivity of the positive almost periodic solution of this model is also considered. Finally, three examples are given to illustrate the main results of this paper.

Existence and global attractivity of positive periodic solutions for a delayed competitive system with the effect of toxic substances and impulses

Changjin Xu, Qianhong Zhang, Maoxin Liao (2013)

Applications of Mathematics

In this paper, a class of non-autonomous delayed competitive systems with the effect of toxic substances and impulses is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantees the existence of at least one positive periodic solution, and by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are established.

Existence and global exponential stability of periodic solutions for general neural networks with time-varying delays.

Yang, Xinsong (2008)

International Journal of Mathematics and Mathematical Sciences

Existence and global stability of positive periodic solutions of a discrete delay competition system.

Huo, Hai-Feng, Li, Wan-Tong (2003)

International Journal of Mathematics and Mathematical Sciences

Existence and Lyapunov stability of periodic solutions for generalized higher-order neutral differential equations.

Ren, Jingli, Cheung, Wing-Sum, Cheng, Zhibo (2011)

Boundary Value Problems [electronic only]

Existence and positivity of solutions for a nonlinear periodic differential equation

Ernest Yankson (2012)

Archivum Mathematicum

We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.

Existence and stability of antiperiodic solution for a class of generalized neural networks with impulses and arbitrary delays on time scales.

Li, Yongkun, Xu, Erliang, Zhang, Tianwei (2010)

Journal of Inequalities and Applications [electronic only]

Existence and stability of periodic solutions for a class of generalized nonautonomous neural networks with distributed delays.

Li, Yongkun, Zhu, Lifei, Liu, Wenxiang (2005)

International Journal of Mathematics and Mathematical Sciences

Existence and Stability of Periodic Solutions for Nonlinear Neutral Differential Equations with Variable Delay Using Fixed Point Technique

Mouataz Billah MESMOULI, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Our paper deals with the following nonlinear neutral differential equation with variable delay $\frac{d}{d t} D u_{t} (t) = p (t) - a (t) u (t) - a (t) g (u (t - τ (t))) - h (u (t), u (t - τ (t))) .$ By using Krasnoselskii’s fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. A sufficient condition is established for the positivity of the above equation. Stability results of this equation are analyzed. Our results extend and complement some results obtained in the work [Yuan, Y., Guo, Z.: On the existence and stability of...

Existence and uniqueness of periodic solutions for a kind of Duffing equation with two deviating arguments

Bingwen Liu (2006)

Annales Polonici Mathematici

We use the coincidence degree to establish new results on the existence and uniqueness of T-periodic solutions for a kind of Duffing equation with two deviating arguments of the form x'' + Cx'(t) + g₁(t,x(t-τ₁(t))) + g₂(t,x(t-τ₂(t))) = p(t).

Existence and uniqueness of periodic solutions for a kind of nonlinear nth order differential equations with delays

Weiwen Shao, Fuxing Zhang, Ya Li (2008)

Annales Polonici Mathematici

By applying the continuation theorem of coincidence degree theory, we establish new results on the existence and uniqueness of 2π-periodic solutions for a class of nonlinear nth order differential equations with delays.

Existence and uniqueness of periodic solutions for a second-order nonlinear differential equation with piecewise constant argument.

Wang, Gen-Qiang, Cheng, Sui Sun (2009)

International Journal of Mathematics and Mathematical Sciences

Existence and uniqueness of periodic solutions for first-order neutral functional differential equations with two deviating arguments.

Xiao, Jinsong, Liu, Bingwen (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and uniqueness of periodic solutions of mixed monotone functional differential equations.

Kang, Shugui, Cheng, Sui Sun (2009)

Abstract and Applied Analysis

Existence and uniqueness of positive periodic solutions of delayed Nicholson's blowflies models

Fei Long, Bingwen Liu (2012)

Annales Polonici Mathematici

This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays. By applying the coincidence degree, some criteria are established for the existence and uniqueness of positive periodic solutions of the model. Moreover, a totally new approach to proving the uniqueness of positive periodic solutions is proposed. In particular, an example is employed to illustrate the main results.

Existence of nonnegative periodic solutions in neutral integro-differential equations with functional delay

Imene Soulahia, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)

Commentationes Mathematicae Universitatis Carolinae

The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay $x^{'} (t) = - \int_{t - τ (t)}^{t} a (t, s) g (x (s)) d s + \frac{d}{d t} Q (t, x (t - τ (t))) + G (t, x (t), x (t - τ (t))) .$ We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for $τ$ , $g$ , $a$ , $Q$ and $G$ to show that this sum of mappings fits into the framework of a modification of Krasnoselskii’s...

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