Growth and oscillation of some polynomials generated by solutions of complex differential equations

Relation between small functions with differential polynomials generated by meromorphic solutions of higher order linear differential equations

“…The present article may be understood as an extension and improvement of the recent article of the authors [14] from usual order to iterated order. The main purpose of this paper is to study the growth and oscillation of the differential polynomial (1.2) generated by meromorphic solutions of equation (1.1).…”

“…Lemma 2.8. [14] Assume f ≡ 0 is a solution of equation (1.1). Then the differential polynomial g f defined in (1.2) satisfies the system of equations…”

Finite Logarithmic Order Meromorphic Solutions of Complex Linear Delay-Differential Equations

“…The concepts of logarithmic order and logarithmic type of entire or meromorphic functions were introduced by Chern, [9,10]. Since then, many authors used them in order to generalize previous results obtained on the growth of solutions of linear difference equations and linear differential equations in which the coefficients are entire or meromorphic functions in the complex plane C of positive order different to zero, see for example [1,6,11,14,19,21,22], their new results were on the logarithmic order, the logarithmic lower order and the logarithmic exponent of convergence, where they considered the case when the coefficients are of zero order see, for example, [2-4, 7, 12, 17, 18, 23]. In this article, we also use these concepts to investigate the lower logarithmic order of solutions to more general homogeneous and non homogeneous linear delay-differential equations, where we generalize those results obtained in [5,8].…”

Properties of higher order differential polynomials generated by solutions of complex differential equations in the unit disc

“…Remark 1.5 For some papers related in the complex plane see [19,22,24] and in the unit disc see [7,9,12] .…”