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Title: On the oscillation of a class of linear homogeneous third order differential equations (English)
Author: Parhi, N.
Author: Das, P.
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 34
Issue: 4
Year: 1998
Pages: 435-443
Summary lang: English
Category: math
Summary: In this paper we have considered completely the equation \[ y^{\prime \prime \prime }+ a(t)y^{\prime \prime }+ b(t)y^\prime + c(t)y=0\,, \qquad \mathrm {(*)}\] where $a\in C^2([\sigma , \infty ), R)$, $b\in C^1([\sigma , \infty ),R)$, $c\in C([\sigma , \infty ), R)$ and $\sigma \in R$ such that $a(t)\le 0$, $b(t)\le 0$ and $c(t)\le 0$. It has been shown that the set of all oscillatory solutions of (*) forms a two-dimensional subspace of the solution space of (*) provided that (*) has an oscillatory solution. This answers a question raised by S. Ahmad and A.  C. Lazer earlier. (English)
Keyword: third order differential equations
Keyword: oscillation
Keyword: nonoscillation
Keyword: asymptotic behaviour of solutions
MSC: 34C10
MSC: 34C11
MSC: 34D05
idZBL: Zbl 0973.34023
idMR: MR1679638
Date available: 2009-02-17T10:15:49Z
Last updated: 2012-05-10
Stable URL:
Reference: [1] Ahmad, S., Lazer, A. C.: On the oscillatory behaviour of a class of linear third order differential equations.J. Math. Anal. Appl. 28(1970), 681-689, MR 40#1646. MR 0248394
Reference: [2] Hanan, M.: Oscillation criteria for a third order linear differential equations.Pacific J. Math. 11(1961), 919-944, MR 26# 2695. MR 0145160
Reference: [3] Jones, G. D.: Properties of solutions of a class of third order differential equations.J. Math. Anal. Appl. 48(1974), 165-169. Zbl 0289.34046, MR 0352608
Reference: [4] Lazer, A. C.: The behaviour of solutions of the differential equation $y^{\prime \prime \prime }+ p(x)y^\prime + q(x)y=0$.Pacific J. Math. 17(1966), 435-466, MR 33#1552. MR 0193332
Reference: [5] Leighton, W., Nehari, Z.: On the oscillation of self adjoint linear differential equations of the fourth order.Trans. Amer. Math. Soc. 89(1958), 325-377. MR 0102639
Reference: [6] Parhi, N., Das, P.: On asymptotic property of solutions of a class of third order differential equations.Proc. Amer. Math. Soc. 110(1990), 387-393. MR 1019279


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