Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Bifurcation of periodic solutions in a nonlinear difference-differential equations of neutral type

Author: Robert K. Brayton
Journal: Quart. Appl. Math. 24 (1966), 215-224
MSC: Primary 34.75; Secondary 34.45
DOI: https://doi.org/10.1090/qam/204800
MathSciNet review: 204800
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Abstract: The existence of a self-sustained periodic solution in the autonomous equation

$\displaystyle u'\left( \tau \right) - \alpha u'\left( {\tau - h} \right) + \bet... ...ma u\left( {\tau - h} \right) = \epsilon f\left( {u\left( \tau \right)} \right)$

is proved under appropriate assumptions on $ \alpha ,\beta ,\gamma ,f$ and $ h$. The method of proof consists in converting this equation into an equivalent nonlinear integral equation and demonstrating the convergence of an appropriate iteration scheme.

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

  • [1] R. Bellman and K. L. Cooke, Differential-difference equations, Academic Press, New York, 1963. MR 0147745
  • [2] N. Krasovskii, On periodic solutions of differential equations involving a time lag, Dokl. Acad. Nauk (N. S.), 114 252-255 (1957). MR 0090733
  • [3] N. Shimanov, Almost periodic solutions in nonlinear systems with retardation, Dokl. Acad. Nauk, S. S. S. R., 125 1203-1206 (1959). MR 0106317
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  • [6] R. K. Brayton, Nonlinear oscillations in a distributed network. To appear in a forthcoming issue of Quart, of Applied Math.

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DOI: https://doi.org/10.1090/qam/204800
Article copyright: © Copyright 1966 American Mathematical Society

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