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Boundedness for solutions of nonlinear periodic differential equations via Moser's twist theorem

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Abstract

We consider the nonlinear periodic differential equation

$$\frac{{d^2 x}}{{dt^2 }} + \beta x^{2n + 1} + a(t)x = p(t), n \geqslant 1,$$

wherea(t) andp(t) are continuous and 1-periodic, β is a positive constant. The purpose of this paper is to prove that all solutions of the above-mentioned equation are bounded fort∈R and there are infinitely many quasi-periodic solutions and an infinity of periodic solutions of minimal periodm, for each positive integerm.

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Authors and Affiliations

  1. Department of Mathematics, Peking University, Beijing, China

    Liu Bin

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  1. Liu Bin
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Bin, L. Boundedness for solutions of nonlinear periodic differential equations via Moser's twist theorem. Acta Mathematica Sinica 8, 91–98 (1992). https://doi.org/10.1007/BF02595021

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  • DOI: https://doi.org/10.1007/BF02595021

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