Estimates of the logarithmic derivative near a singular point and applications

In this paper, we will give estimates near z = 0 for the logarithmic derivative | f (k)(z) / f(z) | where f is a meromorphic function in a region of the form D(0,R) = {z ∈ C : 0 < |z| < R}. Some applications on the growth of solutions of linear differential equations near a singular point are given

Finite and infinite order of growth of solutions to linear differential equations near a singular point

summary:In this paper, we investigate the growth of solutions of a certain class of linear differential equation where the coefficients are analytic functions in the closed complex plane except at a finite singular point. For that, we will use the value distribution theory of meromorphic functions developed by Rolf Nevanlinna with adapted definitions

Iterated order of solutions of certain linear differential equations with entire coefficients

In this paper, we investigate the iterated order of solutions of homogeneous and nonhomogeneous linear differential equations where the coefficients are entire functions and satisfy certain growth conditions

Properties of solutions to linear differential equations with analytic coefficients in the unit disc

In this article we study the growth of solutions of linear differential equations with analytic coefficients in the unit disc. Our investigation is based on the behavior of the coefficients on a neighborhood of a point on the boundary of the unit disc

Orders of solutions of an n-th order linear differential equation with entire coefficients

We study the solutions of the differential equation $$f^{(n)}+A_{n-1}(z) f^{(n-1) }+dots+A_{1}(z)f'+A_{0}(z) f=0,$$ where the coefficients are entire functions. We find conditions on the coefficients so that every solution that is not identically zero has infinite order

Growth of solutions of a class of linear fractional differential equations with polynomial coefficients

This paper is devoted to the study of the growth of solutions of certain class of linear fractional differential equations with polynomial coefficients involving the Caputo fractional derivatives by using the generalized Wiman–Valiron theorem in the fractional calculus

Nonhomogeneous linear differential equations with entire coefficients having the same order and type

In this paper we will investigate the growth of solutions of certain class of nonhomogeneous linear differential equations with entire coefficients having the same order and type. This work improves and extends some previous results in [1], [7] and [9]