Differential and Integral Equations

Almost periodic solutions for a class of Duffing-like systems

Vittorio Coti Zelati, Piero Montecchiari, and Margherita Nolasco

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We prove the existence of infinitely many limit periodic solutions for Duffing-like systems of the type $-\ddot{q} = g(t,q)$, where $g$ is limit periodic in time and has a non-degenerate homoclinic solution to the hyperbolic stationary solution $q \equiv 0$. Moreover, we can deal with almost periodic perturbations of the above class of systems. In this case we prove the existence of almost periodic solutions and we show that these solutions are quasi-periodic whenever the perturbation is quasi periodic.

Article information

Differential Integral Equations, Volume 11, Number 4 (1998), 623-640.

First available in Project Euclid: 30 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C27: Almost and pseudo-almost periodic solutions
Secondary: 34C25: Periodic solutions 37J45: Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods


Coti Zelati, Vittorio; Montecchiari, Piero; Nolasco, Margherita. Almost periodic solutions for a class of Duffing-like systems. Differential Integral Equations 11 (1998), no. 4, 623--640. https://projecteuclid.org/euclid.die/1367341037

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