Qualitative Behaviour of Solutions of Differential Equations



Seshadev Padhi
Mississippi State University
sp377@ra.msstate.edu



Abstract: We establish sufficient conditions for the oscillation of a class linear differential equation of third order of the form

$\displaystyle y^{\prime \prime \prime}+a(t)y^{\prime \prime}+b(t)y^{\prime}+c(t)y=0$

where $ a,b,c \in (\sigma,\infty),R)$, with $ a(t)\leq 0,b(t)\geq 0$ and $ c(t)< 0$ and $ \sigma\in R$. The results improves the observations obtained when $ a(t)\equiv a \leq 0, b(t)\equiv b \geq 0$ and $ c(t)\equiv c <0$ are constants.