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Boundedness of solutions for Duffing equation with low regularity in time

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Abstract

It is shown that all solutions are bounded for Duffing equation \(\ddot x + {x^{2n + 1}} + \sum\limits_{j = 0}^{2n} {{P_j}} \left( t \right){x^j} = 0\), provided that for each n + 1 ≤ j ≤ 2n, P j ∈ Cγ (T1) with γ > 1 − 1/n and for each j with 0 ≤ j ≤ n, P j ∈ L(T1) where T1 = R/Z.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Xiaoping Yuan

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  1. Xiaoping Yuan
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Correspondence to Xiaoping Yuan.

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Project supported by the National Natural Science Foundation of China (No. 11421061).

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Yuan, X. Boundedness of solutions for Duffing equation with low regularity in time. Chin. Ann. Math. Ser. B 38, 1037–1046 (2017). https://doi.org/10.1007/s11401-017-1020-x

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  • DOI: https://doi.org/10.1007/s11401-017-1020-x

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