Periodic solutions of the Rayleigh equation with damping of definite sign

Pierpaolo Omari; Gabriele Villari

Displaying similar documents to “Periodic solutions of the Rayleigh equation with damping of definite sign”

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.

Periodic solutions for second order differential systems with damping

Fabio Zanolin (1981)

Rendiconti del Seminario Matematico della Università di Padova

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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.

On forced periodic oscillations in dissipative Liénard systems

Fabio Zanolin (1983)

Rendiconti del Seminario Matematico della Università di Padova

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Periodic solutions of Liénard equations

Pierpaolo Omari, Fabio Zanolin (1984)

Rendiconti del Seminario Matematico della Università di Padova

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

Abdelouaheb Ardjouni, Ahcène Djoudi (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Let $𝕋$ be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to Burton to prove the existence of periodic solutions on time scale of the nonlinear dynamic equation with variable delay $x^{▵} (t) = - a (t) h (x^{σ} (t)) + c (t) x^{\tilde{▵}} (t - r (t)) + G (t, x (t), x (t - r (t)))$ , $t \in 𝕋$ , where $f^{▵}$ is the $▵$ -derivative on $𝕋$ and $f^{\tilde{▵}}$ is the $▵$ -derivative on $(i d - r) (𝕋)$ . We invert the given equation to obtain an equivalent integral equation from which we define a fixed point mapping written as a sum of a large contraction and a compact...

Existence of $T$ -periodic solutions for a class of lagrangian systems

Elvira Mirenghi, Maria Tucci (1990)

Rendiconti del Seminario Matematico della Università di Padova

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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...