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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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