Fite‐Wintner‐Leighton‐Type Oscillation Criteria for Second‐Order Differential Equations with Nonlinear Damping

Mervan Pašić

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/852180

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:852180

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