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