Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (1): 46-52.

• Articles • Previous Articles     Next Articles

On the Growth of Solutions of f''+Af'+Bf=0, Where A is a Solution of a Second Order Linear Differential Equation

 WU Xiu-Bi1, WU Peng-Cheng2   

  1. 1.Guizhou University, Guiyang 550025|
    2.Guizhou Normal University, Guiyang 550001
  • Received:2011-08-25 Revised:2012-11-23 Online:2013-02-25 Published:2013-02-25
  • Supported by:

    国家自然科学基金(11171080)和贵州省科学技术基金(黔科合J字LKS[2010]07号)资助

Abstract:

Let  A(z) be  a nontrivial solution of f''+P(z)f=0, where P(z) is a polynomial and let B(z) be a transcendental  entire function of  order ρ≤1/2. Then every nontrivial solution of f''+A(z)f'+B(z)f=0 is of infinite order. Moreover, the exponent of convergence of zero-sequence of the product of two linearly independent solutions of f''+A(z)f=0 is of infinite.

CLC Number: 

  • 34M10
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