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Pašić, Mervan

Fite-Wintner-Leighton-type oscillation criteria for second-order differential equations with nonlinear damping. (English) Zbl 1308.34043

Abstr. Appl. Anal. 2013, Article ID 852180, 10 p. (2013).
Summary: 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.

Cited in 8 Documents

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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