Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the stability of solutions of a second-order differential equation


Author: E. Infeld
Journal: Quart. Appl. Math. 32 (1975), 465-467
MSC: Primary 34D05
DOI: https://doi.org/10.1090/qam/445071
MathSciNet review: 445071
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Abstract: This paper deals with the Hill differential equation

$\displaystyle {d^2}y/d{x^2} + \frac{r}{{1 - 2a\cos x + {a^2}}}y = 0$

Although this equation looks more difficult than Mathieu's, it can be dealt with some-what more simply than the latter. Stability criteria are obtained in terms of $ r$ and $ a$ (at least in principle).

References [Enhancements On Off] (What's this?)

  • [1] N. W. McLachlan, Theory and Application of Mathieu Functions, Oxford, at the Clarenden Press, 1947. MR 0021158
  • [2] I. S. Gradshteyn and I. M. Ryshik, Table of integrals, series and products, Academic Press, 1965
  • [3] E. Infeld and G. Rowlands, On the stability of non-linear cold plasma waves II, J. Plasma Phys. 10, 233 (1973)

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Additional Information

DOI: https://doi.org/10.1090/qam/445071
Article copyright: © Copyright 1975 American Mathematical Society


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