Boundedness of solutions for Duffing equation with low regularity in time

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 ∈ C^γ (T¹) with γ > 1 − 1/n and for each j with 0 ≤ j ≤ n, P _j ∈ L(T¹) where T¹ = R/Z.

Keywords

Duffing equation / Boundedness of solutions / Lagrange stability / Moser twist theorem / Quasi-periodic solution

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