Oscillation of solutions of certain ordinary differential equations of $n\textrm {th}$ order
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- by Gerald H. Ryder and David V. V. Wend
- Proc. Amer. Math. Soc. 25 (1970), 463-469
- DOI: https://doi.org/10.1090/S0002-9939-1970-0261091-5
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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
- 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 10.1007/BF01444165
- 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
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 463-469
- MSC: Primary 34.42
- DOI: https://doi.org/10.1090/S0002-9939-1970-0261091-5
- MathSciNet review: 0261091