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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

The existence of a non-trivial periodic solution for the autonomous Rayleigh equation x ¨ + F 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 x ¨ + F x ˙ + g x = e t .

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

Monika Kubicova (1989)

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

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 to a non-linear parametric differential equation of the third order

Jan Andres, Jan Vorácek (1984)

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

Si dimostra un teorema di esistenza di soluzioni periodiche dell'equazione differenziale ordinaria del terzo ordine x ′′′ + a ( t , x , x , x ′′ ) x ′′ + b ( t , x , x , x ′′ ) x + h ( x ) = e ( t , x , x , x ′′ ) con le funzioni a , b , e periodiche in t di periodo ω .

Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces

Nguyen Thieu Huy, Ngo Quy Dang (2016)

Annales Polonici Mathematici

We prove the existence and conditional stability of periodic solutions to semilinear evolution equations of the form u̇ = A(t)u + g(t,u(t)), where the operator-valued function t ↦ A(t) is 1-periodic, and the operator g(t,x) is 1-periodic with respect to t for each fixed x and satisfies the φ-Lipschitz condition ||g(t,x₁) - g(t,x₂)|| ≤ φ(t)||x₁-x₂|| for φ(t) being a real and positive function which belongs to an admissible function space. We then apply the results to study the existence, uniqueness...

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