Growth of solutions of an n-th order linear differential equation with entire coefficients

Kodai Mathematical Journal

Saada Hamouda¹  Benharrat Belaidi¹ 

关键词: Linear differential equations;    entire functions;    finite order of growth;   

DOI  :  10.2996/kmj/1071674457

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(9)We consider a differential equation f(n)+An−1(z)f(n−1)+…+A1(z)f'+A0(z)f=0, where A0(z), ..., An−1(z) are entire functions with A0(z){¬≡}0. Suppose that there exist a positive number μ, and a sequence (zj)j∈N with limj→+∞zj=∞, and also two real numbers α, β (0≤β<α) such that |A0(zj)|≥eα|zj|μ and |Ak(zj)|≤eβ|zj|μ as j→+∞ (k=1, ..., n−1). We prove that all solutions f{¬≡}0 of this equation are of infinite order. This result is a generalization of one theorem of Gundersen ([3], p. 418).

【 授权许可】

Unknown