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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Maintenance of oscillations under the effect of a periodic forcing term
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by Athanassios G. Kartsatos PDF
Proc. Amer. Math. Soc. 33 (1972), 377-383 Request permission

Abstract:

A necessary and sufficient condition is given for the oscillation of all solutions of the differential equation \[ {x^{(n)}} + P(t,x,x’, \cdots ,{x^{(n - 1)}}) = Q(t)\] where ${x_1}P(t,{x_1},{x_2}, \cdots ,{x_n}) > 0$ for every ${x_1} \ne 0$, and Q is a continuous periodic function. This result answers a question recently raised by J. S. W. Wong. It is also shown that a well-known sufficient condition for the existence of at least one nonoscillatory solution of the unperturbed equation guarantees, for a large class of equations, the nonexistence of bounded oscillatory solutions.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 33 (1972), 377-383
  • MSC: Primary 34C10
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0330622-0
  • MathSciNet review: 0330622