Consider the second order nonlinear neutral differential equation with delays: Ε½ . w . E d rdt y t y py t y q q t f y t y s 0, for t g 0, Ο± , where Ε½ . Ε½ . Ε½ . Ε½ . q t , f x are continuous functions, q t G 0, yf y ) 0 if y / 0, and 0p -1, Ε½ . ) 0, ) 0. When f y satisfies either the superlinear or
β¦ LIBER β¦
Necessary and Sufficient Conditions for the Oscillation of Forced Nonlinear Second Order Differential Equations with Delayed Argument
β Scribed by A.H. Nasr
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 150 KB
- Volume
- 212
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
For a special class of the external force g t and nonnegative potential a t , we give necessary and sufficient conditions for the oscillation of all solutions of a nonlinear second order forced differential equation with delayed argument of Ε½ .
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## Abstract Sufficient conditions are established for oscillation of second order super half linear equations containing both delay and advanced arguments of the form equation image where __Ο~Ξ΄~__ (__u__) = |__u__ |^__Ξ΄__ β1^__u__; __Ξ±__ > 0, __Ξ²__ β₯ __Ξ±__, and __Ξ³__ β₯ __Ξ±__ are real numbers; __k