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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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Oscillation of solutions of certain ordinary differential equations of $n\textrm {th}$ order

Authors: Gerald H. Ryder and David V. V. Wend
Journal: Proc. Amer. Math. Soc. 25 (1970), 463-469
MSC: Primary 34.42
MathSciNet review: 0261091
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Abstract | References | Similar Articles | Additional Information

Abstract: Necessary and sufficient conditions are given that all solutions of ${y^{(n)}} + f(t, y) = 0$ which are continuable to infinity are oscillatory in the case $n$ is even and are oscillatory or strongly monotone in the case $n$ is odd. The results generalize to arbitrary $n$ recent results of J. Macki and J. S. W. Wong for the case $n = 2$ and include as special cases results of I. Kiguradze, I. Ličko and M. Švec, and Š. Belohorec.

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

    Š. Belohorec, Oscillatory solutions of certain nonlinear differential equations of the second order, Mat.-Fyz. Časopis Sloven. Akad. Vied 11 (1961), 250-255. (Slovak)
  • I. T. Kiguradze, The capability of certain solutions of ordinary differential equations to oscillate, Dokl. Akad. Nauk SSSR 144 (1962), 33–36 (Russian). MR 0136817
  • ---, The problem of oscillations of solutions of nonlinear differential equations, J. Differential Equations 3 (1967), 773-782.
  • Imrich Ličko and Marko Švec, Le caractère oscillatoire des solutions de l’équation $y^{(n)}+f(x)y^{\alpha }=0,\,n>1$, Czechoslovak Math. J. 13(88) (1963), 481–491 (French, with Russian summary). MR 161001
  • Adolf Kneser, Untersuchungen über die reellen Nullstellen der Integrale linearer Differentialgleichungen, Math. Ann. 42 (1893), no. 3, 409–435 (German). MR 1510784, DOI
  • Jack W. Macki and James S. W. Wong, Oscillation of solutions to second-order nonlinear differential equations, Pacific J. Math. 24 (1968), 111–117. MR 224908

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Keywords: Oscillation of solutions, nonoscillation of solutions, nonlinear differential equations, strongly nonlinear differential equations
Article copyright: © Copyright 1970 American Mathematical Society