Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF Free Access

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] -, 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 (44:7042)
  • [3] G. J. Butler, Oscillation theorems for a nonlinear analogue of Hill's equation, Quart. J. Math. Oxford Ser. (2) 27 (1976), 159-171. MR 0409976 (53:13727)
  • [4] -, Integral averages and the oscillation of second order ordinary differential equations, SIAM J. Math. Anal. 11 (1980), 190-200. MR 556509 (80m:34028)
  • [5] M. K. Grammatikopoulos, Oscillation theorems for second order ordinary differential inequalities and equations with alternating coefficients, An. Stiint. Univ. "Al. I. Cuza" Iasi Sect. I a Mat. 26 (1980), 67-76. MR 582469 (81k:34024)
  • [6] I. V. Kamenev, Some specifically nonlinear oscillation theorems, Mat. Zametki 10 (1971), 129-134. (Russian) MR 0287077 (44:4284)
  • [7] J. S. W. Wong, Oscillation theorems for second order nonlinear differential equations, Bull. Inst. Math. Acad. Sinica 3 (1975), 283-309. MR 0390372 (52:11198)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C15

Retrieve articles in all journals with MSC: 34C15


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

American Mathematical Society