Existence of Periodic Solutions for Nonlinear Neutral Dynamic Equations with Functional Delay on a Time Scale

Abdelouaheb Ardjouni; Ahcène Djoudi

Displaying similar documents to “Existence of Periodic Solutions for Nonlinear Neutral Dynamic Equations with Functional Delay on a Time Scale”

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...

Periodic Solutions of Periodic Retarded Functional Differential Equations

Marcin Pawłowski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) $x^{'} (t) = f (t, x_{t})$ , where f is T-periodic in t. We construct a pair of subsets of ℝ × ℝⁿ called a T-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a T-periodic solution.

Positive periodic solutions of functional differential equations with infinite delay

Changxiu Song (2008)

Annales Polonici Mathematici

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The author applies a generalized Leggett-Williams fixed point theorem to the study of the nonlinear functional differential equation $x^{'} (t) = - a (t, x (t)) x (t) + f (t, x_{t})$ . Sufficient conditions are established for the existence of multiple positive periodic solutions.

Periodic solutions for first order neutral functional differential equations with multiple deviating arguments

Lequn Peng, Lijuan Wang (2014)

Annales Polonici Mathematici

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We consider first order neutral functional differential equations with multiple deviating arguments of the form ${(x (t) + B x (t - δ))}^{'} = g ₀ (t, x (t)) + \sum_{k = 1}^{n} g_{k} (t, x (t - τ_{k} (t))) + p (t)$ . By using coincidence degree theory, we establish some sufficient conditions on the existence and uniqueness of periodic solutions for the above equation. Moreover, two examples are given to illustrate the effectiveness of our results.

Periodic solutions to a non-linear differential equation of the order $2n+1$

Monika Kubicova (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A criterion for the existance of periodic solutions of an ordinary differential equation of order k proved by J. Andres and J. Vorâcek for k = 3 is extended to an arbitrary odd k.

Periodic solutions of the Rayleigh equation with damping of definite sign

Pierpaolo Omari, Gabriele Villari (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The existence of a non-trivial periodic solution for the autonomous Rayleigh equation $\ddot{x} + F (\dot{x}) + g (x) = 0$ is proved, assuming conditions which do not imply that $F (x) x$ has a definite sign for $|x|$ large. A similar result is obtained for the periodically forced equation $\ddot{x} + F (\dot{x}) + g (x) = e (t)$ .

Periodic solutions to a non-linear differential equation of the order $2n+1$

Monika Kubicova (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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A criterion for the existance of periodic solutions of an ordinary differential equation of order k proved by J. Andres and J. Vorâcek for k = 3 is extended to an arbitrary odd k.

Stable periodic solutions in scalar periodic differential delay equations

Anatoli Ivanov, Sergiy Shelyag (2023)

Archivum Mathematicum

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A class of nonlinear simple form differential delay equations with a $T$ -periodic coefficient and a constant delay $τ > 0$ is considered. It is shown that for an arbitrary value of the period $T > 4 τ - d_{0}$ , for some $d_{0} > 0$ , there is an equation in the class such that it possesses an asymptotically stable $T$ -period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The...

Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters

Shu-Gui Kang, Bao Shi, Sui Sun Cheng (2009)

Annales Polonici Mathematici

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Existence of periodic solutions of functional differential equations with parameters such as Nicholson’s blowflies model call for the investigation of integral equations with parameters defined over spaces with periodic structures. In this paper, we study one such equation $ϕ (x) = λ \int_{[x, x + ω] \cap Ω} K (x, y) h (y) f (y, ϕ (y - τ (y))) d y$ , x ∈ Ω, by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.

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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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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The periodic problem for the second order integro-differential equations with distributed deviation

Sulkhan Mukhigulashvili, Veronika Novotná (2021)

Mathematica Bohemica

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We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation $u^{''} (t) = p_{0} (t) u (t) + \int_{0}^{ω} p (t, s) u (τ (t, s)) d s + q (t),$ and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some...