## Abstract and Applied Analysis

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

M. Tamer Şenel

#### Abstract

The oscillation of solutions of the second-order nonlinear dynamic equation $(r(t)({x}^{\Delta }(t){)}^{\gamma }{)}^{\Delta }+p(t)({x}^{\Delta }(t){)}^{\gamma }+f(t,x(g(t)))=0$, with damping on an arbitrary time scale $\mathbb{T}$, 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

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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