一类强迫Mathieu方程解的稳定性和收敛性的最大区间

力学国际期刊(英文) Pub Date : 2020-11-10 DOI:10.4236/wjm.2020.1011015

E. Eze, U. E. Obasi, R. N. Ujumadu, Grace Ihuoma Kalu

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引用次数: 0

摘要

结合Frobenius方法和特征值方法，研究了一类强迫Mathieu方程解的稳定性和收敛性的最大区间。结果表明，平衡点是不稳定的，恢复力导数存在最大边界，证明周期解存在的尖锐条件。此外，Mathieu方程解的收敛性推广和改进了文献中的一些结果。

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Maximum Interval of Stability and Convergence of Solution of a Forced Mathieu’s Equation

This paper investigates the maximum interval of stability and convergence of solution of a forced Mathieu’s equation, using a combination of Frobenius method and Eigenvalue approach. The results indicated that the equilibrium point was found to be unstable and maximum bounds were found on the derivative of the restoring force showing sharp condition for the existence of periodic solution. Furthermore, the solution to Mathieu’s equation converges which extends and improves some results in literature.

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来源期刊

力学国际期刊(英文)

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发文量

275