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boundedness of solutions for a Class of Oscillating Potentials without the Twist Condition

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Acta Mathematica Sinica,English Series 2010年第12期26卷 2387-2398页

作者： Zhi Guo WANG Yi Qian WANG School of Mathematical Sciences Soochow University Suzhou 215006 P. R. China Department of Mathematics Nanjing University Nanjing 210093 P. R. China

In this paper, we prove that the second order differential equation d^2x/dt^2＋x^2n_1f（x）＋p（t）=0with p（t ＋ 1） = p（t）, f（x ＋ T） = f（x） smooth and f（x）〉 0, possesses Lagrangian stability despite of th... 详细信息

关键词： boundedness of solutions oscillating potential twist condition KAM theorem

boundedness of solutions for sublinear reversible systems

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Science China Mathematics 2001年第2期44卷 137-144页

作者：黎雄 Department of Mathematical Sciences Tsinghua University Beijing China

We are concerned with the boundedness of all the solutions for second order differential equation $$\ddot x + f\left( x \right)\dot x + g\left( x \right) = e\left( t \right),$$ , wheref(x) andg(x) are odd, e( t) is odd and 1-periodic, andg(x) satisfies $$Sign \left( x \right) \cdot g\left( x \right) \to + \infty ,\frac{{g\left( x \right)}}{x} \to 0,as\left| x \right| \to + \infty .$$

关键词： boundedness of solutions invariant tori reversible systems

boundedness of solutions for Duffing Equation with Low Regularity in Time

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Chinese Annals of Mathematics,Series B 2017年第5期38卷 1037-1046页

作者： Xiaoping YUAN School of Mathematical Sciences Fudan UniversityShanghai 200433China

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... 详细信息

关键词： Duffing equation boundedness of solutions Lag-range stability Mosertwist theorem Quasi-periodic solution

A Result on the Quasi-periodic solutions of Forced Isochronous Oscillators at Resonance

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Chinese Annals of Mathematics,Series B 2015年第4期36卷 523-542页

作者： Bin LIU Yingchao TANG LMAM School of Mathematical Sciences Peking University

In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g and e are regular, described precisely in the *** a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.

关键词： Isochronous oscillators Repulsive singularity Invariant curves Timereversibility Quasi-periodic solutions Lazer-Landesman conditions boundedness of solutions

THE　EXISTENCE　OF　PERIODIC　solutions　FOR　A　CLASS　OF　FUNCTIONAL　DIFFERENTIAL　EQUATIONS　AND　THEIR　APPLICATION

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Applied Mathematics and Mechanics(English Edition) 1994年第1期15卷 49-59页

作者：赵杰民黄克累陆启韶 Department of Applied Mathematics and Physics Peking University of Aeronautics and Astronautics Beijing

In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s p... 详细信息

关键词： retarded functional differential equation. periodic solution boundedness of solutions

Invariant Tori and boundedness in Asymmetric Oscillations

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Acta Mathematica Sinica,English Series 2003年第4期19卷 765-782页

作者： XinPingWANG SchoolofMathematicsSciences BeijingUniversityBeijing100871P.R.China

In this paper, we are concerned with the boundedness of all the solutions ofthe equation x' + ax^+ - bx^- + φ(x) = p(t), where p(t) is a smooth 2π-periodic function, a and bare positive constants, and the perturbati... 详细信息

关键词： boundedness of solutions quasi-periodic solutions Moser's small twisttheorem