Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (3): 401-408.

• Articles •     Next Articles

On the Growth of Solutions of Some Higher Order Linear Differential Equations

 LONG Jian-Ren1,2, ZHU Jun3, LI Xiao-Man1   

  1. 1.School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001;
    2.Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing |100190;
    3.School of Mathematical Sciences, Peking University, Beijing |100871
  • Received:2011-05-24 Revised:2012-10-20 Online:2013-06-25 Published:2013-06-25
  • 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)资助

Abstract:

In this paper, we shall involve the deficient value in investigating the growth of  solutions of the linear differential equation f (k)+Ak-1(z)f(k-1)+…+A1(z)f' +A0(z)f=0,
where Aj(z) (j=0, 1, …, k-1) are entire functions, and we obtain some results which improves some earlier results. More specifically, we estimate the lower bounded of hyper-order of solutions of the equation if every solution f(≠0) of the equation is of infinite order.

Key words: Complex differential equations, Entire function, Deficient value, Hyper-order

CLC Number: 

  • 34M10
Trendmd