It is shown that all solutions are bounded for Duffing equation s＋ x^2n＋1＋j=0∑^2n Pj（t）x^j=0,provided that for each n ＋ 1≤j≤2n,Pj ∈ C^γ（T^1） with γ〉1-1/n and for each j with 0 ≤ j ≤ n,Pj ∈L （T^1） w...It is shown that all solutions are bounded for Duffing equation s＋ x^2n＋1＋j=0∑^2n Pj（t）x^j=0,provided that for each n ＋ 1≤j≤2n,Pj ∈ C^γ（T^1） with γ〉1-1/n and for each j with 0 ≤ j ≤ n,Pj ∈L （T^1） where T^1=R/Z.展开更多
The existence of Mather sets(generalized quasiperiodic solutions and uNlinked periodicsolutions)for sublinear Duffing equations is shown. Here the approach is based on the use ofaction-angle variables and the applicat...The existence of Mather sets(generalized quasiperiodic solutions and uNlinked periodicsolutions)for sublinear Duffing equations is shown. Here the approach is based on the use ofaction-angle variables and the application of a generalized version of Aubry-Mather theoremon semi-cylinder with finite twist assumption.展开更多
The boundedness of all solutions is shown for Duffing-type equations $\frac{{d^2 x}}{{dt^2 }} + x^{2n + 1} + \sum\limits_{j = 0}^{2n} {x^j p_j (t) = 0, n \geqslant 1,} $ wherep 1,p 2,...,p 2n are of period 1 and of Li...The boundedness of all solutions is shown for Duffing-type equations $\frac{{d^2 x}}{{dt^2 }} + x^{2n + 1} + \sum\limits_{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.展开更多
本文对解析映射证明了一个不动点定理(称为扭转弯曲定理),其中弯曲条件取代了经典扭转定理(参考Ding W.Y.,A generalization of the Poincare-Birkhoff theorem,Proc.Amer.Soc.,1983,88:341-346)中的保面积条件;然后用本文的扭转弯曲定...本文对解析映射证明了一个不动点定理(称为扭转弯曲定理),其中弯曲条件取代了经典扭转定理(参考Ding W.Y.,A generalization of the Poincare-Birkhoff theorem,Proc.Amer.Soc.,1983,88:341-346)中的保面积条件;然后用本文的扭转弯曲定理证明了一类耗散的Duffing方程拥有高阶的次调和解.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11421061)
文摘It is shown that all solutions are bounded for Duffing equation s＋ x^2n＋1＋j=0∑^2n Pj（t）x^j=0,provided that for each n ＋ 1≤j≤2n,Pj ∈ C^γ（T^1） with γ〉1-1/n and for each j with 0 ≤ j ≤ n,Pj ∈L （T^1） where T^1=R/Z.
文摘The existence of Mather sets(generalized quasiperiodic solutions and uNlinked periodicsolutions)for sublinear Duffing equations is shown. Here the approach is based on the use ofaction-angle variables and the application of a generalized version of Aubry-Mather theoremon semi-cylinder with finite twist assumption.
文摘The boundedness of all solutions is shown for Duffing-type equations $\frac{{d^2 x}}{{dt^2 }} + x^{2n + 1} + \sum\limits_{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.
文摘本文对解析映射证明了一个不动点定理(称为扭转弯曲定理),其中弯曲条件取代了经典扭转定理(参考Ding W.Y.,A generalization of the Poincare-Birkhoff theorem,Proc.Amer.Soc.,1983,88:341-346)中的保面积条件;然后用本文的扭转弯曲定理证明了一类耗散的Duffing方程拥有高阶的次调和解.
