Gen-Qiang Wang, Sui Sun Cheng (2002)
Annales Polonici Mathematici
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A priori bounds are established for periodic solutions of an nth order Rayleigh equation with delay. From these bounds, existence theorems for periodic solutions are established by means of Mawhin's continuation theorem.
Raffoul, Y. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Weiwen Shao, Fuxing Zhang, Ya Li (2008)
Annales Polonici Mathematici
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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.
Wang, Genqiang, Yan, Jurang (2001)
Journal of Applied Mathematics and Stochastic Analysis
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Sergio Invernizzi, Fabio Zanolin (1978)
Mathematische Zeitschrift
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Yasunori Okada (2012)
Banach Center Publications
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For some classes of periodic linear ordinary differential equations and functional equations, it is known that the existence of a bounded solution in the future implies the existence of a periodic solution. In order to think on such phenomena for hyperfunction solutions to linear functional equations, we introduced a notion of bounded hyperfunctions, and translated the problems into the problems on analytic solutions to some equations in complex domains. In this article,...
Tianwei Zhang, Yongzhi Liao (2017)
Kybernetika
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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.
S. Invernizzi, F. Zanolin (1979)
Rendiconti del Seminario Matematico della Università di Padova
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Mouataz Billah MESMOULI, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Our paper deals with the following nonlinear neutral differential equation with variable delay 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...
Fei Long, Bingwen Liu (2012)
Annales Polonici Mathematici
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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.
Glizer, Valery Y.
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We consider the singularly perturbed set of periodic functional-differential matrix Riccati equations, associated with a periodic linear-quadratic optimal control problem for a singularly perturbed delay system. The delay is small of order of a small positive multiplier for a part of the derivatives in the system. A zero-order asymptotic solution to this set of Riccati equations is constructed and justified.
Božena Dorociaková, Rudolf Olach (2016)
Open Mathematics
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The paper deals with the existence of positive ω-periodic solutions for a class of nonlinear delay differential equations. For example, such equations represent the model for the survival of red blood cells in an animal. The sufficient conditions for the exponential stability of positive ω-periodic solution are also considered.
Wu, Jun, Liu, Yicheng (2006)
Discrete Dynamics in Nature and Society
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Mihály Pituk, John Ioannis Stavroulakis (2025)
Czechoslovak Mathematical Journal
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A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.
J. Ma, J. Wu (2010)
Mathematical Modelling of Natural Phenomena
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We study the coexistence of multiple periodic solutions for an analogue of the integrate-and-fire neuron model of two-neuron recurrent inhibitory loops with delayed feedback, which incorporates the firing process and absolute refractory period. Upon receiving an excitatory signal from the excitatory neuron, the inhibitory neuron emits a spike with a pattern-related delay, in addition to the synaptic delay. We present a theoretical framework...