On the Existence and Uniqueness of Periodic Solutions of Differential Delay Equations.

Sergio Invernizzi; Fabio Zanolin

Displaying similar documents to “On the Existence and Uniqueness of Periodic Solutions of Differential Delay Equations.”

Periodic solutions of nth order delay Rayleigh equations

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.

Periodic solutions for some delay differential equations appearing in models of power systems

Bingwen Liu, Lihong Huang (2005)

Annales Polonici Mathematici

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The authors use coincidence degree theory to establish some new results on the existence of T-periodic solutions for the delay differential equation x''(t) + a₁x'(t) + a₂(xⁿ(t))' + a₃x(t)+ a₄x(t-τ) + a₅xⁿ(t) + a₆xⁿ(t-τ) = f(t), which appears in a model of a power system. These results are of practical significance.

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

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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.

Positive periodic solutions in neutral nonlinear differential equations.

Raffoul, Y. (2007)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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A notion of boundedness for hyperfunctions and Massera type theorems

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,...

Existence of periodic solution for first order nonlinear neutral delay equations.

Wang, Genqiang, Yan, Jurang (2001)

Journal of Applied Mathematics and Stochastic Analysis

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Periodic solutions of a differential delay equation of Rayleigh type

S. Invernizzi, F. Zanolin (1979)

Rendiconti del Seminario Matematico della Università di Padova

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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

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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...