Abstract and Applied Analysis

Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

M. Tamer Şenel

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Abstract

The oscillation of solutions of the second-order nonlinear dynamic equation ( r ( t ) ( x Δ ( t ) ) γ ) Δ + p ( t ) ( x Δ ( t ) ) γ + f ( t , x ( g ( t ) ) ) = 0 , with damping on an arbitrary time scale T , is investigated. The generalized Riccati transformation is applied for the study of the Kamenev-type oscillation criteria for this nonlinear dynamic equation. Several new sufficient conditions for oscillatory solutions of this equation are obtained.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 253107, 18 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365174050

Digital Object Identifier
doi:10.1155/2012/253107

Mathematical Reviews number (MathSciNet)
MR2947665

Zentralblatt MATH identifier
1246.34090

Citation

Şenel, M. Tamer. Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 253107, 18 pages. doi:10.1155/2012/253107. https://projecteuclid.org/euclid.aaa/1365174050


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