Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales

Quanwen Lin, Baoguo Jia and Qiru Wang

Abstract and Applied Analysis, 2010, vol. 2010, 1-10

Abstract:

We will establish a new interval oscillation criterion for second-order half-linear dynamic equation ( r ( t ) [ x Δ ( t ) ] α ) Δ + p ( t ) x α ( σ ( t ) ) = f ( t ) on a time scale T which is unbounded, which is a extension of the oscillation result for second order linear dynamic equation established by Erbe et al. (2008). As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation ( [ x ′ ( t ) ] α ) ′ + c sin t x α ( t ) = cos ⠡ t , where α = p / q , p , q are odd positive integers.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:294194

DOI: 10.1155/2010/294194

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