一类二阶微分方程的解的有界性
Boundedness of Solutions for a Class of Second-Order Periodic Systems

作者: 江舜君 :南京工业大学理学院,南京;

关键词: 解的有界性奇点小扭转定理Boundedness of Solutions Singularity Small Twist Theorem

摘要:
本文我们将研究下面的二阶周期系统:,其中含有一个奇点。通过Ortega的小扭转定理(引理9),对做恰当的假设,我们得到拟周期解的存在性,从而得出所有解的有界性。
>In this paper, we study the following second-order periodic system: where has a singularity. Under some assumptions on the , by Ortega small twist theorem (Lemma 9), we obtain the existence of quasi-periodic solutions and boundedness of all the solutions.

文章引用: 江舜君 (2013) 一类二阶微分方程的解的有界性。 理论数学, 3, 379-387. doi: 10.12677/PM.2013.36058

参考文献

[1] Capietto, A., Dambrosio, W. and Liu, B. (2009) On the boundedness of solutions to a nonlinear singularoscillator. Zeitschrift für Angewandte Mathematik und Physik, 60, 1007-1034.

[2] Morris, G.R. (1976) A case of boundedness of Littlewood’s problem on oscillatory differential equations. Bulletin of the Australian Mathe- matical Society, 14, 71-93.

[3] Levi, M. (1991) Quasiperiodic motions in superquadratic time-periodic potential. Communications in Mathematical Physics, 143, 43-83.

[4] Liu, B. (1989) Boundedness for solutions of nonlinear Hill’s equations with periodic forcing terms via Moser’s twist theorem. Journal of Dif- ferential Equations, 79, 304-315.

[5] Kunze, M., Kupper, T. and Liu, B. (2001) Boundedness and unboundedness of solutions for reversible oscillatorsat resonance. Nonlinearity, 14, 1105-1122.

[6] Liu, B. (2005) Quasiperiodic solutions of semilinear lienard reversible oscillators. Discrete and Continuous Dynamical Systems, 12, 137-160.

[7] Ortega, R. (1999) Boundedness in a piecewise linear oscillator and a variant of the small twist theorem. Proceedings London Mathematical Society, 79, 381-413.

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