Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
third order differential equations; oscillation; nonoscillation; asymptotic behaviour of solutions
third order differential equations; oscillation; nonoscillation; asymptotic behaviour of solutions
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.
References:
[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
[2] Hanan, M.: Oscillation criteria for a third order linear differential equations. Pacific J. Math. 11(1961), 919-944, MR 26# 2695. MR 0145160
[3] Jones, G. D.: Properties of solutions of a class of third order differential equations. J. Math. Anal. Appl. 48(1974), 165-169. MR 0352608 | Zbl 0289.34046
[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
[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
[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
Search
Partner of
