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Article Dans Une Revue Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 14 (2007), Adv. in Dyn. Systems Année : 2007

Singular perturbations of Partial Differential Equations on the Torus. Applications to Quasi-Periodic and Almost Periodic Solutions of Variational Problems

Résumé

In this paper we consider an equation of type $q''(t)=\partial_2 V(t,q(t))$, where $V$ is quasi-periodic (q.p.) in $t$, uniformly w.r.t. to $q$, is convex w.r.t. $q$ for each $t$. We look for q.p. solutions $q:\R \to \IH$ (where $\IH$ is an Hilbert space) to this equation. By using the formalism introduced by the Physician Percival, it is possible to transform this problem in a elliptic degenerate Partial Differential Equation on the torus. By using a singular perturbation method, we obtain existence results under technical assumptions on $V$.
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Dates et versions

hal-00617463 , version 1 (29-08-2011)

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  • HAL Id : hal-00617463 , version 1

Citer

Joël Blot, Denis Pennequin. Singular perturbations of Partial Differential Equations on the Torus. Applications to Quasi-Periodic and Almost Periodic Solutions of Variational Problems. Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 14 (2007), Adv. in Dyn. Systems, 2007, Suppl. 2, pp.97-102. ⟨hal-00617463⟩
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