数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 1177-1186.doi: 10.1016/S0252-9602(13)60072-7

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SECTORIAL OSCILLATION THEORY OF LINEAR DIFFERENTIAL EQUATIONS

吴昭君|陈裕先   

  1. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China|School of Mathematics and Computer Science, Xinyu University, Xinyu 338004, China
  • 收稿日期:2011-09-21 修回日期:2012-04-17 出版日期:2013-07-20 发布日期:2013-07-20
  • 基金资助:

    This research was partially supported by the NSF of Jiangxi Province (2010GZC0187), NSF of Educational Department of the Hubei Province (T201009, Q20112807) and NFS of China (11201395).

SECTORIAL OSCILLATION THEORY OF LINEAR DIFFERENTIAL EQUATIONS

 WU Zhao-Jun, CHEN Yu-Xian   

  1. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China|School of Mathematics and Computer Science, Xinyu University, Xinyu 338004, China
  • Received:2011-09-21 Revised:2012-04-17 Online:2013-07-20 Published:2013-07-20
  • Supported by:

    This research was partially supported by the NSF of Jiangxi Province (2010GZC0187), NSF of Educational Department of the Hubei Province (T201009, Q20112807) and NFS of China (11201395).

摘要:

In this paper, the sectorial oscillation of the solutions of higher order homo-geneous linear differential equations
f(k) + An−2(z)f (k−2) +… + A1(z)' + A0(z)f = 0
with infinite order entire function coefficients is studied. Results are obtained to extend some results in [19] and [18].

关键词: radial exponent of convergence, iterated order, sectorial oscillation, Borel direction

Abstract:

In this paper, the sectorial oscillation of the solutions of higher order homo-geneous linear differential equations
f(k) + An−2(z)f (k−2) +… + A1(z)' + A0(z)f = 0
with infinite order entire function coefficients is studied. Results are obtained to extend some results in [19] and [18].

Key words: radial exponent of convergence, iterated order, sectorial oscillation, Borel direction

中图分类号: 

  • 30D35