Non-existence of finite order solutions of \(w''+e^{-z}w'+Q(z)w=0\). (English) Zbl 0554.34003

Amemiya, Ichiro; Ozawa, Mitsuru

Hokkaido Math. J. 10, 1-17 (1981).

The main result of the paper refers to the growth estimate of solutions of \(w''+F(z)w=0\) along a ray around to which F(z) is regular. Applying this result the authors obtain the following nice one: The differential equation \(w''+e^{-z}w'+(a_ nz^ n+a_ pz^ p+...+a_ 0)w=0\), where \(a_ n\neq 0\), \(p\geq 0\) and either \(n\geq 2p+3\), or \(n=2p+1\), or \(p=0\), \(a_ 0=0\), \(n=2\), does not admit any entire solution of finite order.

Reviewer: G.Karakostas

MSC:

34M99	Ordinary differential equations in the complex domain
30D15	Special classes of entire functions of one complex variable and growth estimates

Keywords:

growth estimate; entire solution of finite order