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On oscillations for solutions of $ n$th order differential equations


Author: H. Onose
Journal: Proc. Amer. Math. Soc. 33 (1972), 495-500
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1972-0296419-5
MathSciNet review: 0296419
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Abstract: Necessary and sufficient conditions are given that all solutions of $ {x^{(n)}} + f(t,x,x', \cdots ,{x^{(n - 2)}}) = 0$ are oscillatory for n even and are oscillatory or tend monotonically to zero as $ t \to \infty $ for n odd. The results generalize recent results of J. S. W. Wong and G. H. Ryder and D. V. V. Wend.


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

  • [1] H. Onose, Oscillatory properties of solutions of even order differential equations, Pacific J. Math. 38 (1971), 747-757. MR 0306615 (46:5737)
  • [2] -, Oscillatory property of ordinal differential equations of arbitrary order, J. Differential Equations 7 (1970), 454-458. MR 41 #2116. MR 0257465 (41:2116)
  • [3] G. H. Ryder and D. V. V. Wend, Oscillation of solutions of certain ordinary differential equations of nth order, Proc. Amer. Math. Soc. 25 (1970), 463-469. MR 41 #5710. MR 0261091 (41:5710)
  • [4] J. S. W. Wong, On second order nonlinear oscillation, Funkcial. Ekvac. 11 (1968), 207-234, MR 39 #7221. MR 0245915 (39:7221)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0296419-5
Keywords: Oscillatory, nonoscillatory, generalized strongly continuous, monotonically to zero
Article copyright: © Copyright 1972 American Mathematical Society

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