Advances in Difference Equations
Volume 2010 (2010), Article ID 586312, 23 pages
doi:10.1155/2010/586312
Oscillation behavior of third-order neutral Emden-Fowler delay dynamic equations on time scales
Zhenlai Han1
, Tongxing Li1
, Shurong Sun1
and Chenghui Zhang4
1School of Science, University of Jinan, Jinan, Shandong 250022, China
4School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
Abstract
We will establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations (r(t)(x(t)−a(t)x(τ(t)))ΔΔ)Δ+p(t)xγ(δ(t))=0 on a time scale 𝕋, where γ>0 is a quotient of odd positive integers with r, a, and p real-valued positive rd-continuous functions defined on 𝕋. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. Some examples are considered to illustrate the main results.