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On the growth of solutions of certain linear differential equations. (English) Zbl 0759.34005
Suppose $$g_ j$$, $$0\leq j\leq n-1$$, and $$h$$ are entire functions and that for some $$k$$, $$0\leq k\leq n-1$$, the order of $$g_ k$$ does not exceed $${1\over 2}$$ and does exceed the order of $$h$$ and the order of all other $$g_ j$$. It is shown that then every solution of the differential equation $$f^{(n)}+\sum_{j=0}^{n-1}g_ j f^{(j)}=h$$ is either a polynomial or an entire function of infinite order. This generalizes a previous result of the author for second order equations.

##### MSC:
 34M99 Ordinary differential equations in the complex domain 30D20 Entire functions of one complex variable (general theory) 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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