Relations between the small functions and the solutions of certain second-order differential equations
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Date
2007-08-07
Authors
Liu, Huifang
Mao, Zhiqiang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper, we investigate the relations between the small functions and the solutions, first, second derivatives, and differential polynomial of the solutions to the differential equation
ƒ″ + A1ₑP(z) ƒ′ + A(0ₑQ(z) ƒ = 0,
where P(z) = αₙzⁿ + ⋅⋅⋅ + α0, Q(z) = bₙzⁿ + ⋅⋅⋅ + b0 are polynomials with degree n (n ≥ 1), αi, bi (i = 0, 1,..., n), αnbn ≠ 0 are complex constants, Aj(z) ≢ 0 (j = 0, 1) are entire functions with σ(Aj) < n.
Description
Keywords
Entire function, Exponent of convergence of the zero-sequence
Citation
Liu, H., & Mao, Z. (2007). Relations between the small functions and the solutions of certain second-order differential equations. <i>Electronic Journal of Differential Equations, 2007</i>(108), pp. 1-11.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.