Geodesic
On the oscillation of a class of linear homogeneous third order differential equations
Archivum mathematicum, Tome 34 (1998) no. 4, pp. 435-443
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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.
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.
Classification : 34C10, 34C11, 34D05
Keywords: third order differential equations; oscillation; nonoscillation; asymptotic behaviour of solutions 
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Parhi, N.; Das, P. On the oscillation of a class of linear homogeneous third order differential equations. Archivum mathematicum, Tome 34 (1998) no. 4, pp. 435-443. http://geodesic.mathdoc.fr/item/ARM_1998_34_4_a2/

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