Rad HAZU, Matematičke znanosti, Vol. 26 (2022), 139-153.

DIFFERENTIAL POLYNOMIALS GENERATED BY SOLUTIONS OF SECOND ORDER NON-HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS

Benharrat Belaïdi

Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem, B. P 227 Mostaganem, Algeria
e-mail: benharrat.belaidi@univ-mosta.dz

Abstract.   This paper is devoted to studying the growth and the oscillation of solutions of the second order non-homogeneous linear differential equation

f'' + Aea1z f' + B(z) ea2z f = F(z) ea1z,

where A, a1, a2 are complex numbers, B(z) (≢ 0) and F(z) (≢ 0) are entire functions with order less than one. Moreover, we investigate the growth and the oscillation of some differential polynomials generated by solutions of the above equation.

2020 Mathematics Subject Classification.   34M10, 30D35.

Key words and phrases.   Differential polynomial, linear differential equations, entire solutions, order of growth, exponent of convergence of zeros, exponent of convergence of distinct zeros.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/y26kecl839

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