Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (2): 224-230.

• Articles • Previous Articles     Next Articles

An Oscillation Result for Higher Order Linear Differential Equations with One Dominant Coefficient

 YUAN Wen-Jun   

  1. 广州大学数学系 广州 510405 中国科学院数学与系统科学研究院数学研究所 北京 100080
  • Online:2003-04-25 Published:2003-04-25
  • Supported by:

    中国科学院数学与系统科学研究院、国家自然科学基金(19971091)、广东省自然科学基金(020586)和广州大学重点项目(LGZD0108)资助

Abstract:

 The following theorem is known result, if the coefficients are entire (e.g. Bank  and Laine for k=2,ρ(A_0)<1/2; Rossi for k=2,ρ(A_0)=1/2; Langley and Hellers tein and coworkers for k≥2,ρ(A_0)≤1/2 In this paper the author will use some new method to  prove.Theorem Suppose that A_j(j=1,2,,k-2) are meromorphic functions  with finite poles. If the order ρ(A_0) of A_0 is not greater than 1/2, and ρ(A_j)<ρ(A_0) for j=1,2,,k-2, then Eq.(1.1) wi th k≥2 cannot have two linearly independent solutions each with zero sequen ce having finite exponent of convergence.

Key words: Meromorphic function, Growth order, Convergence exponent, Dominant coefficient.

CLC Number: 

  • 30D35
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