On the Growth of Solutions of Higher Order Linear Differential Equations


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New Zealand Journal of Mathematics

Vol. 42, (2012), Pages 27-36

Nan Wu

Department of Mathematics,

School of Science,

China University of Mining and Technology (Beijing),

Beijing, 100083,

People's Republic of China.


Ye-Zhou Li

School of Science,

Beijing University of Posts and Tele Communications,

Beijing, 100876,

People's Republic of China.


Abstract In this paper, we discuss the growth order of the meromorphic solution of the differential equation A_n(z)f^{(n)}(z)+\cdots+A_1(z)f'(z)+A_0f(z)=F(z) with meromorphic coefficients A_0(z), A_1(z),\cdots, A_n(z) in some angular regions and generalize a result in the complex plane \mathbb{C}.

Keywords Differential equations, Meromorphic solutions, Order, Angular region.

Classification (MSC2000) Primary 30D10; Secondary 30D20, 30B10, 34M05.

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