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  • 标题:Oscillation criteria for a generalized Emden-Fowler dynamic equation on time scales
  • 本地全文:下载
  • 作者:Yunlong Shi ; Zhenlai Han ; Ying Sun
  • 期刊名称:Advances in Difference Equations
  • 印刷版ISSN:1687-1839
  • 电子版ISSN:1687-1847
  • 出版年度:2016
  • 卷号:2016
  • 期号:1
  • 页码:3
  • DOI:10.1186/s13662-015-0701-6
  • 语种:English
  • 出版社:Hindawi Publishing Corporation
  • 摘要:In this paper, we consider the second-order Emden-Fowler neutral delay dynamic equation ( r ( t ) z Δ ( t ) α − 1 z Δ ( t ) ) Δ + q ( t ) x ( δ ( t ) ) β − 1 x ( δ ( t ) ) = 0 $$\bigl(r(t)\bigl\vert z^{\Delta}(t)\bigr\vert ^{\alpha-1}z^{\Delta}(t) \bigr)^{\Delta}+q(t)\bigl\vert x \bigl(\delta(t) \bigr)\bigr\vert ^{\beta-1}x \bigl(\delta(t) \bigr)=0 $$ on time scales, where z ( t ) = x ( t ) + p ( t ) x ( τ ( t ) ) $z(t)=x(t)+p(t)x (\tau(t) )$ and β ≥ α > 0 $\beta\geq\alpha>0$ are constants. By means of the Riccati transformation and inequality technique, some oscillation criteria are established, which extend and improve some known results in the literature.
  • 关键词:oscillation ; second-order ; Emden-Fowler equation ; neutral delay dynamic equation ; time scale
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