The Lagrangian Stability for a Class of Second‐Order Quasi‐Periodic Reversible Systems

Yanling Shi and Jia Li

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: We study the following two‐order differential equation, (Φp(x′))′ + f(x, t)Φp(x′) + g(x, t) = 0, where Φp(s) = |s|(p−2)s, p > 0. f(x, t) and g(x, t) are real analytic functions in x and t, 2aπp− periodic in x, and quasi‐periodic in t with frequencies (ω1, …, ωm). Under some odd‐even property of f(x, t) and g(x, t), we obtain the existence of invariant curves for the above equations by a variant of small twist theorem. Then all solutions for the above equations are bounded in the sense of supt∈R|x′(t)|

Date: 2011
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https://doi.org/10.1155/2011/489148

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:489148

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