Hellerstein, Simon; Miles, Joseph; Rossi, John On the growth of solutions of certain linear differential equations. (English) Zbl 0759.34005 Ann. Acad. Sci. Fenn., Ser. A I, Math. 17, No. 2, 343-365 (1992). 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. Reviewer: S.Hellerstein (Madison, WI) Cited in 2 ReviewsCited in 19 Documents 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 Keywords:Nevanlinna characteristic; entire functions; differential equation; polynomial; infinite order PDFBibTeX XMLCite \textit{S. Hellerstein} et al., Ann. Acad. Sci. Fenn., Ser. A I, Math. 17, No. 2, 343--365 (1992; Zbl 0759.34005) Full Text: DOI