PDF(481 KB)
PDF(481 KB)
PDF(481 KB)
次线性非对称Duffing方程的不变环面
Invariant Tori of Sublinear Asymmetric Duffing Equations
利用Moser扭转定理，在一定的光滑性条件下，证明了次线性非对称Duffing方程x"+a（x+）1/3-b（x-）1/3+φ（x）=p（t）无穷多不变环面的存在性，从而得到拉格朗日稳定性，其中扰动项φ（x）有界，而强迫项p（t）是周期函数.
By using Moser's twist theorem, under some smoothness conditions, we prove the existence of infinitely many invariant tori and so the Lagrange stability for the sublinear asymmetric Duffing equations x"+a(x+)1/3-b(x-)1/3+φ(x)=p(t), where the perturbation term φ(x) is bounded, while the forced term p(t) is periodic in t.
不变环面 / 解的有界性 / 次线性非对称Duffing方程 / 扭转定理 {{custom_keyword}} /
invariant tori / boundedness of solutions / sublinear asymmetric Duffing equation / twist theorem {{custom_keyword}} /
[1] Alonso M. J., Ortega R., Roots of unity and unbounded motions of an asymmetric oscillator, J. Differ. Equ., 1998, 143:201-220.
[2] Dieckerhoff R., Zehnder E., Boundedness for solutions via the twist-theorem, Ann. Scuola Norm. Sup. Pisa, Cl. Sci., 1987, 14:79-95.
[3] Jiao L., Piao D. X., Wang Y. Q., Boundedness of the general semilinear Duffing equations via the twist-theorem, J. Diff. Equ., 2012, 252:91-113.
[4] Lazer A. C., McKenna P. J., Large-amplitude periodic oscillations in suspension bridge:some new connections with nonlinear analysis, SIAM Rev., 1990, 32(4):537-578.
[5] Liu B., Boundedness in asymmetric oscillations, J. Math. Anal. Appl., 1999, 231:355-373.
[6] Moser J., On invariant curves of area preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. Ⅱ, 1962, 1962:1-20.
[7] Ortega R., Asymmetric oscillators and twist mappings, J. Lond. Math. Soc., 1996, 53:325-342.
[8] Wang X. M., Aubry-Mather sets for sublinear asymmetric Duffing equations (in Chinese), Sci. Sin. Math., 2012, 42(1):13-21.
[9] Wang X. P., Invariant tori and boundedness in asymmetric oscillations, Acta. Math. Sin. Engl. Ser., 2003, 19:765-782.
[10] Wang Z. H., Wang Y. Q., Li H., Boundedness of solutions for Duffing equations with asymmetric superlinear restoring terms, Chin. Ann. Math. Ser. A, 2002, 23(2):187-196.
[11] You J. G., Boundedness for solutions of superlinear Duffing equations via the twist theorem, Sci. China Ser. A, 1992, 35(4):399-412.
国家自然科学基金资助项目（11571327，11971059）
/
| 〈 |
|
〉 |
