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

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  • Quanwen Lin
  • Baoguo Jia
  • Qiru Wang

Abstract

We will establish a new interval oscillation criterion for second‐order half‐linear dynamic equation (r(t)[xΔ(t)] α) Δ + p(t)xα(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) ′ + csintxα(t) = cos t, where α = p/q, p, q are odd positive integers.

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Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:294194
DOI: 10.1155/2010/294194
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