In this paper, oscillation and asymptotic behaviour of solutions of $$y^{\text{'}\text{'}\text{'}}+a\left(t\right)y^{\text{'}\text{'}}+b\left(t\right)y^{\text{'}}+c\left(t\right)y=0$$ have been studied under suitable assumptions on the coefficient functions $a,b,c\in C\left(\right[\sigma ,\infty ),R)$, $\sigma \in R$, such that $a\left(t\right)\ge 0$, $b\left(t\right)\le 0$ and $c\left(t\right)<0$.

Our aim in this paper is to obtain a new oscillation criterion for equation $$y^{\text{'}\text{'}\text{'}}+p\left(t\right)y^{\text{'}}+q\left(t\right)y=0$$ with a nonnegative coefficients which extends and improves some oscillation criteria for this equation. In the special case of equation (*), namely, for equation $y^{\text{'}\text{'}\text{'}}+q\left(t\right)y=0$, our results solve the open question of $Chanturiya$.