Some new oscillation criteria for a general class of second-order differential equations with nonlinear damping are shown. Except some general structural assumptions on the coefficients and nonlinear terms, we additionally assume only one sufficient condition (of Fite-Wintner-Leighton type). It is different compared to many early published papers which use rather complex sufficient conditions. Our method contains three items: classic Riccati transformations, a pointwise comparison principle, and a blow-up principle for sub- and supersolutions of a class of the generalized Riccati differential equations associated to any nonoscillatory solution of the main equation.
"Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping." Abstr. Appl. Anal. 2013 1 - 10, 2013. https://doi.org/10.1155/2013/852180