%0 Journal Article
%T Necessary and sufficient conditions for the oscillation a third-order differential equation
%A Pitambar Das
%A Jitendra Kumar Pati
%J Electronic Journal of Differential Equations
%D 2010
%I Texas State University
%X We show that under certain restrictions the following three conditions are equivalent: The equation $$ y'''+a(t)y''+b(t)y'+c(t)y=f(t) $$ is oscillatory. The equation $$ x'''+a(t)x''+b(t)x'+c(t)x=0 $$ is oscillatory. The second-order Riccati equation $$ z''+3zz'+a(t)z'=z^3+a(t)z^2+b(t)z+c(t) $$ does not admit a non-oscillatory solution that is eventually positive. Furthermore, we obtain sufficient conditions for the above statements to hold, in terms of the coefficients. These conditions are sharp in the sense that they are both necessary and sufficient when the coefficients $a(t), b(t), c(t)$ are constant.
%K Oscillation
%K non-oscillation
%K third order differential equations
%U http://ejde.math.txstate.edu/Volumes/2010/174/abstr.html