International Journal of Differential Equations

Oscillation Theorems for Second-Order Damped Nonlinear Differential Equations

Hui-Zeng Qin and Yongsheng Ren

Full-text: Open access

Abstract

We present new oscillation criteria for the differential equation of the form [ r ( t ) U ( t ) ] + p ( t ) k 2 ( x ( t ) , x ( t ) ) | x ( t ) | ν U ( t ) + q ( t ) ϕ ( x ( g 1 ( t ) ) , x ( g 2 ( t ) ) ) f ( x ( t ) ) = 0 , where U ( t ) = k 1 ( x ( t ) , x ( t ) ) | x ( t ) | α 1 x ( t ) , α β , ν = ( β α ) / ( α + 1 ) . Our research is different from most known ones in the sense that H function is not employed in our results, though Riccati's substitution and its generalized forms are used. Our criteria which are established under quite general assumptions are an extension for previous results. In particular, by taking β = α , the above-mentioned equation can be reduced into the various types of equations concerned by people currently.

Article information

Source
Int. J. Differ. Equ., Volume 2009 (2009), Article ID 714357, 15 pages.

Dates
Received: 26 September 2008
Revised: 28 January 2009
Accepted: 23 March 2009
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399812

Digital Object Identifier
doi:10.1155/2009/714357

Mathematical Reviews number (MathSciNet)
MR2525714

Zentralblatt MATH identifier
1207.34083

Citation

Qin, Hui-Zeng; Ren, Yongsheng. Oscillation Theorems for Second-Order Damped Nonlinear Differential Equations. Int. J. Differ. Equ. 2009 (2009), Article ID 714357, 15 pages. doi:10.1155/2009/714357. https://projecteuclid.org/euclid.ijde/1485399812


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