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Solutions of linear differential equations in the unit disc
  • 期刊名称:J. Math. Resear. Appl.
  • 时间:2014.11.15
  • 页码:729-735
  • 分类:O175.1[理学—数学;理学—基础数学] O174.52[理学—数学;理学—基础数学]
  • 作者机构:[1]College of Mathematics and Information Science, Jiangxi Normal University, Jiangxi 330022, P. R. China
  • 相关基金:Supported by the National Natural Science Foundation of China (Grant Nos. 11301232; 11171119) and the Natural Science Foundation of Jiangxi Province (Grant No. 20132BAB211009).Acknowledgements The authors would like to thank the anonymous referees for their valuable suggestions and comments to improve this article.
  • 相关项目:复域差分, 差分方程和微分方程的研究
中文摘要:

In this paper,we consider the growth of solutions of some homogeneous and nonhomogeneous higher order differential equations.It is proved that under some conditions for entire functions F,Aji and polynomials Pj(z),Qj(z)(j=0,1,…,k-1;i=1,2)with degree n≥1,the equation fk+(Ak-1,1(z)epk-1(z)+Ak-1,2(z)eQk-1(z)/fk-1+…+(A0,1(z)ePo(z)+A0,2(z)eQ0(z))f=F,where k≥2,satisfies the properties:When F ≡0,all the non-zero solutions are of infinite order;when F=0,there exists at most one exceptional solution fo with finite order,and all other solutions satisfy λ(f)=λ(f)=σ(f)=∞.

英文摘要:

In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj(z), Oj(z) (j = 0, 1,..., k - 1; i = 1, 2) with degree n ≥ 1, the equation f(k) + (Ak-l,1 (z)e pk-l(z) +Ak-1,2 (z)eQk-l(z))f(x-1) +...+ (A0,1 (z)eP0(z) + A0,2(z)eQ0(z))f = F, where k ≥ 2, satisfies the properties: When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ(f) = A(f) = σ(f) = ∞.

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