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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Oscillation and nonoscillation criteria for delay differential equations
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by Á. Elbert and I. P. Stavroulakis PDF
Proc. Amer. Math. Soc. 123 (1995), 1503-1510 Request permission

Abstract:

Oscillation and nonoscillation criteria for the first-order delay differential equation \[ x’(t) + p(t)x(\tau (t)) = 0,\quad t \geq {t_0},\tau (t) < t,\] are established in the case where \[ \int _{\tau (t)}^t {p(s)ds \geq \frac {1}{e}\quad {\text {and}}\quad \lim \limits _{t \to \infty } \int _{\tau (t)}^t {p(s)ds = \frac {1}{e}.} } \]
References
  • Á. Elbert, Comparison theorem for first-order nonlinear differential equations with delay, Studia Sci. Math. Hungar. 11 (1976), no. 1-2, 259–267 (1978). MR 545115
  • Á. Elbert and I. P. Stavroulakis, Oscillations of first order differential equations with deviating arguments, Recent trends in differential equations, World Sci. Ser. Appl. Anal., vol. 1, World Sci. Publ., River Edge, NJ, 1992, pp. 163–178. MR 1180110, DOI 10.1142/9789812798893_{0}013
  • R. G. Koplatadze and T. A. Chanturiya, Oscillating and monotone solutions of first-order differential equations with deviating argument, Differentsial′nye Uravneniya 18 (1982), no. 8, 1463–1465, 1472 (Russian). MR 671174
  • Gerasimos Ladas, Sharp conditions for oscillations caused by delays, Applicable Anal. 9 (1979), no. 2, 93–98. MR 539534, DOI 10.1080/00036817908839256
  • A. D. Myškis, Linear homogeneous differential equations of the first order with retarded argument, Uspehi Matem. Nauk (N.S.) 5 (1950), no. 2(36), 160–162 (Russian). MR 0036423
  • A. D. Myshkis, Lineĭ nye differentsial′nye uravneniya s zapazdyvayushchim argumentom, 2nd ed., Izdat. “Nauka”, Moscow, 1972 (Russian). MR 0352648
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1503-1510
  • MSC: Primary 34K15
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1242082-1
  • MathSciNet review: 1242082