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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: 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.

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    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