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The existence of oscillatory solutions for the equation $ d\sp{2}y/dt\sp{2}+q(t)y\sp{r}=0,\,0<r<1$


Author: Kuo Liang Chiou
Journal: Proc. Amer. Math. Soc. 35 (1972), 120-122
MSC: Primary 34C15
DOI: https://doi.org/10.1090/S0002-9939-1972-0301292-2
MathSciNet review: 0301292
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Abstract: This paper gives sufficient conditions for the existence of oscillatory solutions in the sublinear case of the second order differential equation $ {d^2}y/d{t^2} + q(t){y^r} = 0$, where $ q(t)$ is non-negative and continuous and $ 0 < r < 1$. We use the technique of [3, Theorem 3.1] and obtain a result which extends [2, Corollary 1], [3, Theorem 3.1], and [3, Theorem 3.2].


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  • [1] S. Belohorec, On some properties of the equation $ y''(x) + f(x){y^\alpha }(x) = 0,0 < \alpha < 1$, Mat. Časopis Sloven. Akad. Vied. 17 (1967), 10-19. MR 35 #5703. MR 0214854 (35:5703)
  • [2] C. V. Coffman and J. S. W. Wong, Second order nonlinear oscillations, Bull. Amer. Math. Soc. 75 (1969), 1379-1382. MR 40 #449. MR 0247180 (40:449)
  • [3] J. W. Heidel and Don B. Hinton, The existence of oscillatory solutions for a non-linear differential equation, SIAM J. Math. Anal, (to appear). MR 0340721 (49:5472)

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DOI: https://doi.org/10.1090/S0002-9939-1972-0301292-2
Keywords: Oscillation
Article copyright: © Copyright 1972 American Mathematical Society

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