Boundedness of solutions for Duffing-type equation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Boundedness of solutions for Duffing-type equation

Authors:	Xiaoping Yuan

Affiliation:	(1) Department of Mathematics, Fudan University, 200433 Shanghai, China

Abstract:	The boundedness of all solutions is shown for Duffing-type equations $frac{{d^2 x}}{{dt^2 }} + x^{2n + 1} + sumlimits_{j = 0}^{2n} {x^j p_j (t) = 0, n geqslant 1,}$ wherep ₁,p ₂,...,p _2n are of period 1 and of Lipschitzian continuity andp _n+1,...,p _2n are of Zygmundian continuity. This conclusion implies that the boundedness phenomenon for the Duffing-type equations does not require the smoothness in the time-variable, thus answering the question posed by Dieckerhoff and Zehnder.

Keywords:	Duffing-type equation boundedness of solution Moser’ s twist theorem
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