The growth of solutions of \(f''+e^{-z}f'+Q(z)f=0\) where the order \((Q)=1\). (English) Zbl 1054.34139

Chen, Zongxuan

Sci. China, Ser. A 45, No. 3, 290-300 (2002).

Summary: This paper investigates the growth of solutions of the equation \(f'' + e -z f' + Q(z)f = 0\) where the order \((Q) = 1\). When \(Q(z) = h(z)e^{bz}\) \(h(z)\) is a nonzero polynomial, \(b\neq -1\) is a complex constant, every solution of the above equation has infinite order and the hyper-order 1. We improve results due to M. Frei, M. Ozawa, G. Gundersen and J. K. Langley.

MSC:

34M10	Oscillation, growth of solutions to ordinary differential equations in the complex domain
30D05	Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory