Hokkaido Mathematical Journal

On the order and hyper-order of meromorphic solutions of higher order linear differential equations

Maamar ANDASMAS and Benharrat BELAÏDI

Full-text: Open access

Abstract

In this paper, we investigate the order of growth of solutions of the higher order linear differential equation

f(k) + Σk-1j=0 (hjePj(z) + dj) f(j) = 0,

where Pj(z) (j = 0,1,…,k-1) are nonconstant polynomials such that deg Pj = n ≥ 1 and hj(z), dj(z) (j = 0,1,…,k-1) with h0 ≢ 0 are meromorphic functions of finite order such that max {ρ (hj),ρ(dj): j = 0,1,…,k-1} < n. We prove that every meromorphic solution f ≢ 0 of the above equation is of infinite order. Then, we use the exponent of convergence of zeros or the exponent of convergence of poles of solutions to obtain an estimation of the hyper-order of solutions.

Article information

Source
Hokkaido Math. J., Volume 42, Number 3 (2013), 357-383.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1384273387

Digital Object Identifier
doi:10.14492/hokmj/1384273387

Mathematical Reviews number (MathSciNet)
MR3137390

Zentralblatt MATH identifier
1291.34149

Subjects
Primary: 34M10: Oscillation, growth of solutions 30D35: Distribution of values, Nevanlinna theory

Keywords
Linear differential equations Meromorphic solutions Order of growth Hyper-order

Citation

ANDASMAS, Maamar; BELAÏDI, Benharrat. On the order and hyper-order of meromorphic solutions of higher order linear differential equations. Hokkaido Math. J. 42 (2013), no. 3, 357--383. doi:10.14492/hokmj/1384273387. https://projecteuclid.org/euclid.hokmj/1384273387


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