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

Sulkhan Mukhigulashvili; Veronika Novotná

Displaying similar documents to “The periodic problem for the second order integro-differential equations with distributed deviation”

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.

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.

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 of nonlinear differential systems by the method of averaging

Zhanyong Li, Qihuai Liu, Kelei Zhang (2020)

Applications of Mathematics

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In many engineering problems, when studying the existence of periodic solutions to a nonlinear system with a small parameter via the local averaging theorem, it is necessary to verify some properties of the fundamental solution matrix to the corresponding linearized system along the periodic solution of the unperturbed system. But sometimes, it is difficult or it requires a lot of calculations. In this paper, a few simple and effective methods are introduced to investigate the existence...

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.

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.

Analysis of periodic solutions for nonlinear coupled integro-differential systems with variable delays

Bouzid Mansouri, Abdelouaheb Ardjouni, Ahcene Djoudi (2022)

Commentationes Mathematicae Universitatis Carolinae

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The objective of this work is the application of Krasnosel'skii's fixed point technique to prove the existence of periodic solutions of a system of coupled nonlinear integro-differential equations with variable delays. An example is given to illustrate this work.

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.

On generalized periodic solutions of linear differential equations of order n

J. Ligęza (1977)

Annales Polonici Mathematici

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Periodic solutions of differential equations in the cylindrical space

Stanisław Sędziwy (1972)

Annales Polonici Mathematici

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The existence of periodic solutions of an autonomous second order non-linear differential equation

G. J. Butler (1974)

Annales Polonici Mathematici

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Periodic solutions of x" + f(μ, x) = 0

G. J. Butler, H. I. Freedman (1979)

Annales Polonici Mathematici

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

Bingwen Liu (2006)

Annales Polonici Mathematici

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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).

Periodic and Almost Periodic Solutions of Integral Inclusions

Radosław Pietkun (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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The existence of a continuous periodic and almost periodic solutions of the nonlinear integral inclusion is established by means of the generalized Schauder fixed point theorem.