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Oscillation Results for a Second Order Damped Differential Equation with Nonmonotonous Nonlinearity

โœ Scribed by Mokhtar Kirane; Yuri V. Rogovchenko


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
138 KB
Volume
250
Category
Article
ISSN
0022-247X

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โœฆ Synopsis


We present new oscillation criteria for a nonlinear second order differential equation with a damping term. An essential feature of our results is that we do not require the nonlinearity to be nondecreasing. Furthermore, as opposed to the ลฝ recent results by S.


๐Ÿ“œ SIMILAR VOLUMES


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We present new oscillation criteria for the second order nonlinear perturbed differential equations. These criteria are of a high degree of generality and they extend and unify a number of existing results.

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Oscillation criteria for the nonlinear second-order ordinary differential equation with damping x + p t x + f x = 0 are given. The results are extensions of integral averaging technique of Kamenev and include earlier results of Yeh, Yan, and Chen.

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โœ Jitsuro Sugie; Kazuhisa Kita ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 167 KB

The purpose of this paper is to solve the oscillation problem for the nonlinear Euler differential equation t 2 x + g x = 0 and the extended equation x + a t g x = 0. Here g x satisfies the sign condition xg x > 0 if x = 0, but is not assumed to be monotone. We give necessary and sufficient conditio