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

N. Parhi and P. Das

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

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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