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关于一类非多项式位势的Littlewood问题(英文) 被引量：2

ON LITTLEWOOD'S PROBLEM FOR A CLASS OF NONPOLYNOMIAL POTENTIALS
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摘要 本文证明了方程+x^(2n+1)+P_x(x,t)=0所有解的有界性,其中n≥1,P(x,t)是关于两个变量x与t都是光滑的1-周期函数. In this paper,we consider the boundedness of all solutions for the equation +x^(2n+1)+P_x(x,t)=0,where P(x,t) is a smooth 1-periodic function with respect to (x,t) and n≥1.
作者 金慧萍 魏宝社
机构地区 义乌工商职业技术学院 南京大学数学系
出处 《南京大学学报（数学半年刊）》 CAS 2008年第2期178-189,共12页 Journal of Nanjing University(Mathematical Biquarterly)
关键词 解的有界性 非多项式位势 标准变换 Moser扭转定理 boundedness of solutions nonpolynomial potentials canonical transformation Moser's twist theorem
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献24

  • 1Zai-jiu Shang.A Note on the KAM Theorem for Symplectic Mappings[J]. Journal of Dynamics and Differential Equations . 2000 (2)
  • 2Yiqian Wang,Jiangong You.Boundedness of solutions for polynomial potentials withC 2 time dependent coefficients[J]. ZAMP Zeitschrift für angewandte Mathematik und Physik . 1996 (6)
  • 3Liu Bin.Boundedness for solutions of nonlinear periodic differential equations via Moser’s twist theorem[J]. Acta Mathematica Sinica . 1992 (1)
  • 4Mark Levi.Quasiperiodic motions in superquadratic time-periodic potentials[J]. Communications in Mathematical Physics . 1991 (1)
  • 5Liu B,Wang Y Q.Invariant Torus in Nonlinear Oscillation. Scientia Sinica . 1999
  • 6Shang Z J.A Note on the KAM Theorem for Symplectic Mappings. Journal of Dynamics and Differential Equations . 2000
  • 7Wang Y Q.Boundedness of Solutions in Asymmetric Oscillations via the Twist Theorem. Acta Mathematica . 2003
  • 8Wang Y,You J.Boundedness of Solutions in Polynomial Potentials with C~2 Coefficients. Zeitschrift fur Angewandte Mathematik und Physik . 1996
  • 9You J.Boundedness of Solutions of Super-linear Duffing‘s Equations. Scientia Sinica . 1991
  • 10Yuan R,Yuan X P.Boundedness of Solutions for a Class of Nonlinear Differential Equations of Second Order via Moser‘s Twist Theorem. Nonlinear Analysis . 2001

同被引文献22

  • 1Littlewood J. Unbounded solutions of y^n +g(y) =p(t) [J]. J London Math Soc,1966,41 (1) :491-496.
  • 2Morris G. A case of boundedness in littlewood's problem on oscillatory differenial equations [ J ]. Bull Austral Math Soc, 1976,14 (1) :71-93.
  • 3Dieckerhoff R ,Zehnder E. Boundedness of solutions via the twist theorem[ J]. Ann Scuola Norm Sup Pisa, 1987,14( 1 ) :79-95.
  • 4Levi M. Quasi-periodic motions in superquadratic periodic potentials[ J ]. Comm Math Phys, 1991,143 (1):43-83.
  • 5Levi M. KAM theory for particles in periodic potentials[ J ]. Ergod Th & Dynam Sys, 1990,10(4) :777-785.
  • 6Liu Bin. Boundedness for solutions of nonlinear Hill's equations with periodic forcing terms via Moser's twist theorem [ J ]. Differential Equations, 1989,79 ( 2 ) : 304-315.
  • 7Liu Bin. Boundedness of solutions of nonlinear periodic differential equations via Moser's twist theorem [ J ]. Acta Mathematica Sinca New Series,1992,8( 1 ) :91-98.
  • 8Wang Yiqian, You Jiangong. Boundedness of solutions in polynomial potentials with C^2 coefficients[ J ]. ZAMP, 1996,47 (6) :943-952.
  • 9You Jiangong. Boundedness of solutions of super-linear Duffing's equations[ J]. Scientia Sinica, 1991,8 :805-817.
  • 10Yuan Xiaoping. lnvariant torus of Duffing equation[D]. 北京:北京大学,1995.

引证文献2

南京大学学报（数学半年刊）
2008年 第2期

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