Rectifiable oscillations of self-adjoint and damped linear differential equations of second-order

Mervan Pašic, Satoshi Tanaka

研究成果: Article査読

12 被引用数 (Scopus)

抄録

Asymptotic and oscillatory behaviours near x=0 of all solutions y=y(x) of self-adjoint linear differential equation (Ppq): (py')'+qy=0 on (0,T], will be studied, where p=p(x) and q=q(x) satisfy the so-called Hartman-Wintner type condition. We show that the oscillatory behaviour near x=0 of (Ppq) is characterised by the nonintegrability of q/p on (0,T). Moreover, under this condition, we show that the rectifiable (resp. unrectifiable) oscillations near x=0 of (Ppq) are characterised by the integrability (resp. nonintegrability) of q/p34 on (0,T). Next, some invariant properties of rectifiable oscillations in respect to the Liouville transformation are proved. Also, Sturm's comparison type theorem for the rectifiable oscillations is stated. Furthermore, previous results are used to establish such kind of oscillations for damped linear second-order differential equation y'+g(x)y'+f(x)y=0, and especially, the Bessel type damped linear differential equations are considered. Finally, some open questions are posed for the further study on this subject.

本文言語English
ページ(範囲)27-42
ページ数16
ジャーナルJournal of Mathematical Analysis and Applications
381
1
DOI
出版ステータスPublished - 2011 9月 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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