Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 337-348
Guizhou Normal University, School of Mathematical Sciences
Guiyang, 550001, P.R. China; jrlong@gznu.edu.cn, and
Beijing University of Posts and Telecommunications,
School of Computer Sciences and School of Sciences
Beijing, 100876, P.R. China; longjianren2004 'at' 163.com
Guizhou Normal University, School of Mathematical Sciences
Guiyang, 550001, P.R. China; 578609214 'at' qq.com
Guizhou Normal University, School of Mathematical Sciences
Guiyang, 550001, P.R. China; basicmath 'at' 163.com
Guizhou Normal University, School of Mathematical Sciences
Guiyang, 550001, P.R. China; 1150012097 'at' qq.com
Abstract. We prove that every nontrivial solution of f'' + A(z)f' + Q(z)f = 0 is of infinite order, where A(z) is an entire function satisfying λ(A) < ρ(A) < ∞ and some restrictions, and Q(z) is a non-constant polynomial. This result gives partial solutions to a question posed by Gundersen. Related results are also given.
2010 Mathematics Subject Classification: Primary 34M10; Secondary 30D35.
Key words: Complex differential equation, polynomial, infinite order, asymptotic growth.
Reference to this article: J. Long, L. Shi, X. Wu and S. Zhang: On a question of Gundersen concerning the growth of solutions of linear differential equations. Ann. Acad. Sci. Fenn. Math. 43 (2018), 337-348.
https://doi.org/10.5186/aasfm.2018.4315
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