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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 of the third order parametric differential equations involving large nonlinearities

Ján Andres, Vladimír Vlček (1991)

Mathematica Slovaca

Periodic solutions of the third-order differential equation with right-hand side in the form of nonlinear restoring term plus general gradient-like part

Ján Andres (1991)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Periodic solutions of $x " + f (x) x^{' 2 n} + g (x) = 0$ with arbitrarily large period

J. W. Heidel (1971)

Annales Polonici Mathematici

Periodic solutions of $x " + f (x) x^{' m} + g (x) = 0$

W. R. Utz (1971)

Annales Polonici Mathematici

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

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

Annales Polonici Mathematici

Periodic Solutions on hypersurfaces and a result by C. Viterbo.

H. Hofer, E. Zehnder (1987)

Inventiones mathematicae

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

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 $x^{\prime\prime\prime}+a(t,x,x^{\prime},x^{\prime\prime})x^{\prime\prime}+b(t,% x,x^{\prime},x^{\prime\prime})x^{\prime}+h(x)=e(t,x,x^{\prime},x^{\prime\prime})$ con le funzioni $a$ , $b$ , $e$ periodiche in $t$ di periodo $\omega$ .

Periodic solutions to a singular abstract differential equation

Ivan Straškraba, Otto Vejvoda (1974)

Czechoslovak Mathematical Journal

Periodic solutions to abstract differential equations

Ivan Straškraba, Otto Vejvoda (1973)

Czechoslovak Mathematical Journal

Periodic solutions to certain evolution inequalities

Joachim Naumann (1977)

Czechoslovak Mathematical Journal

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 $ℝ^{m} \times 𝕋^{n}$ . A large class of nonhomotopic periodic solutions has been found.

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Periodic solutions of some second order differential systems

Periodic Solutions of Superquadratic Hamiltonian Systems with Bounded Forcing Terms.

Periodic solutions of the equation $x^{''} (t) + g (x (t)) = p (t)$

Periodic solutions of the Rayleigh equation with damping of definite sign

Periodic solutions of the third order parametric differential equations involving large nonlinearities

Periodic solutions of the third-order differential equation with right-hand side in the form of nonlinear restoring term plus general gradient-like part

Periodic solutions of $x " + f (x) x^{' 2 n} + g (x) = 0$ with arbitrarily large period

Periodic solutions of $x " + f (x) x^{' m} + g (x) = 0$

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

Periodic Solutions on hypersurfaces and a result by C. Viterbo.

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

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

Periodic solutions to a singular abstract differential equation

Periodic solutions to abstract differential equations

Periodic solutions to certain evolution inequalities

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

Periodic solutions to Lagrangian system

Periodic solutions to nonlinear differential equations.

Periodic solutions to retarded and partial functional differential equations.

Periodic solutions to second order differential equations of Liénard type with jumping nonlinearities

Currently displaying 81 – 100 of 119