New oscillation criteria for second-order neutral dynamic equations on time scales via Riccati substitution (Q424588)

The authors consider the second-order nonlinear neutral functional dynamic equation NEWLINE\[NEWLINE(p(t)([y(t)+r(t)y(\tau(t))]^{\Delta})^{\gamma})^{\Delta}+f(t,y(\delta(t)))=0NEWLINE\]NEWLINE on a time-scale \(T\) and establish some new sufficient conditions for oscillation. This type of equation has not been studied yet, so the main results in this paper are new. Also, the obtained results cover the cases when \(\delta(T)>t\) and when \(\delta(T)\leq t\). The results in this paper can be applied to any time-scale.