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 \[ {d^2}y/d{x^2} + \frac {r}{{1 - 2a\cos x + {a^2}}}y = 0\] 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).
- N. W. McLachlan, Theory and Application of Mathieu Functions, Oxford, at the Clarenden Press, 1947. MR 0021158
I. S. Gradshteyn and I. M. Ryshik, Table of integrals, series and products, Academic Press, 1965
E. Infeld and G. Rowlands, On the stability of non-linear cold plasma waves II, J. Plasma Phys. 10, 233 (1973)
N. W. McLachlan, Theory and application of Mathieu functions, Clarendon, 1947
I. S. Gradshteyn and I. M. Ryshik, Table of integrals, series and products, Academic Press, 1965
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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Article copyright:
© Copyright 1975
American Mathematical Society
