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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