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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...

Periodic solutions to Lagrangian system

Oleg Zubelevich (2018)

Commentationes Mathematicae Universitatis Carolinae

A classical mechanics Lagrangian system with even Lagrangian is considered. The configuration space is a cylinder m × 𝕋 n . A large class of nonhomotopic periodic solutions has been found.

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