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Oscillation theorems for a second order sublinear ordinary differential equation


Author: Takeshi Kura
Journal: Proc. Amer. Math. Soc. 84 (1982), 535-538
MSC: Primary 34C15
DOI: https://doi.org/10.1090/S0002-9939-1982-0643744-8
MathSciNet review: 643744
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Abstract | References | Similar Articles | Additional Information

Abstract: New oscillation criteria are given for the differential equation

$\displaystyle u'' + a(t)\vert u{\vert^\alpha }\operatorname{sgn} u = 0,\quad 0 < \alpha < 1,$

where $ a(t)$ is allowed to take on negative values for arbitrarily large $ t$.

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

  • [1] S. Belohorec, Oscillatory solutions of certain nonlinear differential equations of the second order, Mat.-Fyz. Časopis Sloven. Akad. Vied. 11 (1961), 250-255.
  • [2] Štefan Belohorec, Two remarks on the properties of solutions of a nonlinear differential equation, Acta Fac. Rerum Natur. Univ. Comenian. Math. 22 (1969), 19–26. MR 0289855
  • [3] G. J. Butler, Oscillation theorems for a nonlinear analogue of Hill’s equation, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 106, 159–171. MR 0409976, https://doi.org/10.1093/qmath/27.2.159
  • [4] G. J. Butler, Integral averages and the oscillation of second order ordinary differential equations, SIAM J. Math. Anal. 11 (1980), no. 1, 190–200. MR 556509, https://doi.org/10.1137/0511017
  • [5] M. K. Grammatikopoulos, Oscillation theorems for second order ordinary differential inequalities and equations with alternating coefficients, An. Ştiinţ. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat. (N.S.) 26 (1980), no. 1, 67–76. MR 582469
  • [6] I. V. Kamenev, Certain specifically nonlinear oscillation theorems, Mat. Zametki 10 (1971), 129–134 (Russian). MR 0287077
  • [7] James S. W. Wong, Oscillation theorems for second order nonlinear differential equations, Bull. Inst. Math. Acad. Sinica 3 (1975), no. 2, 283–309. MR 0390372

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0643744-8
Keywords: Oscillation, oscillatory solution, nonlinear, sublinear differential equation
Article copyright: © Copyright 1982 American Mathematical Society