On the growth of solutions of a class of second-order complex differential equations

In this paper, we consider the differential equation f ″ + h ( z ) e P ( z ) f ′ + Q ( z ) f = 0 , where h ( z ) and Q ( z ) ≢ 0 are meromorphic functions, P ( z ) is a non-constant polynomial. Assume that Q ( z ) has an infinite deficient value and finitely many Borel directions. We give some condi...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2013; no. 1; p. 188
Main Authors Yi, Cai Feng, Liu, Xu-Qiang, Xu, Hong Yan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 27.06.2013
BioMed Central Ltd
Subjects
Analysis
Difference and Functional Equations
Functional Analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
deficient value
complex differential equation
meromorphic function
hyper-order
Borel direction
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Summary:In this paper, we consider the differential equation f ″ + h ( z ) e P ( z ) f ′ + Q ( z ) f = 0 , where h ( z ) and Q ( z ) ≢ 0 are meromorphic functions, P ( z ) is a non-constant polynomial. Assume that Q ( z ) has an infinite deficient value and finitely many Borel directions. We give some conditions on P ( z ) which guarantee that every solution f ≢ 0 of the equation has infinite order. MSC: 34AD20, 30D35.
ISSN:1687-1847
1687-1847
DOI:10.1186/1687-1847-2013-188