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Proceedings of the American Mathematical Society

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Oscillation of solutions of certain ordinary differential equations of $ n{\rm 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: 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?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0261091-5
Keywords: Oscillation of solutions, nonoscillation of solutions, nonlinear differential equations, strongly nonlinear differential equations
Article copyright: © Copyright 1970 American Mathematical Society