On the oscillation of differential equations with an oscillatory coefficient

Harris, B. J.; Kong, Q.

doi:10.1090/S0002-9947-1995-1283552-4

On the oscillation of differential equations with an oscillatory coefficient

Authors: B. J. Harris and Q. Kong
Journal: Trans. Amer. Math. Soc. 347 (1995), 1831-1839
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9947-1995-1283552-4
MathSciNet review: 1283552
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We derive lower bounds for the distance between consecutive zeros of solutions of

$\displaystyle ( * )\quad y'' + q(t)y = 0$

when

takes both positive and negative values. We apply our results to the limit point/limit circle classifications of

[1] W. A. Coppel, Disconjugacy, Lecture Notes in Mathematics, Vol. 220, Springer-Verlag, Berlin-New York, 1971. MR 0460785
[2] B. J. Harris, On an inequality of Lyapunov for disfocality, J. Math. Anal. Appl. 146 (1990), no. 2, 495–500. MR 1043117, https://doi.org/10.1016/0022-247X(90)90319-B
[3] Philip Hartman, Ordinary differential equations, 2nd ed., Birkhäuser, Boston, Mass., 1982. MR 658490
[4] Man Kam Kwong, On Lyapunov’s inequality for disfocality, J. Math. Anal. Appl. 83 (1981), no. 2, 486–494. MR 641347, https://doi.org/10.1016/0022-247X(81)90137-2
[5] Man Kam Kwong, On certain Riccati integral equations and second-order linear oscillation, J. Math. Anal. Appl. 85 (1982), no. 2, 315–330. MR 649178, https://doi.org/10.1016/0022-247X(82)90004-X
[6] W. T. Patula and J. S. W. Wong, An 𝐿^{𝑝}-analogue of the Weyl alternative, Math. Ann. 197 (1972), 9–28. MR 0299865, https://doi.org/10.1007/BF01427949
[7] Ju Rang Yan, On the distance between zeroes and the limit-point problem, Proc. Amer. Math. Soc. 107 (1989), no. 4, 971–975. MR 984825, https://doi.org/10.1090/S0002-9939-1989-0984825-5