# Article

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Keywords:
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:
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