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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