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On the oscillation of a class of linear homogeneous third
order differential equations

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*
N. Parhi and P. Das
*

** Address.**
Department of Mathematics, Berhampur University,
Berhampur - 760 007, INDIA

** E-mail:**

**Abstract.**
In this paper we have considered completely the equation
$$
y^{\prime\prime\prime}+ a(t)y^{\prime\prime}+ b(t)y^\prime +
c(t)y=0\,,
\tag{*}
$$
where $a\in C^2([\si, \infty), R)$, $b\in C^1([\si, \infty),R)$,
$c\in C([\si, \infty), R)$ and $\si \in R$ such that $a(t)\leq
0$, $b(t)\leq 0$ and $c(t)\leq 0$. 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.

**AMSclassification.**
34C10, 34C11

**Keywords.**
Third order differential equations, oscillation, nonoscillation,
asymptotic behaviour of solutions