On non-normal solutions of linear differential equations
@inproceedings{Grohn2016OnNS, title={On non-normal solutions of linear differential equations}, author={Janne Grohn}, year={2016} }
Normality arguments are applied to study the oscillation of solutions of f ′′ +Af = 0, where the coefficient A is analytic in the unit disc D and supz∈D(1 − |z| )|A(z)| < ∞. It is shown that such differential equation may admit a non-normal solution having prescribed uniformly separated zeros.
6 Citations
On the Construction of Solutions of Linear Differential Equations According to Given Sequences
- MathematicsUkrainian Mathematical Journal
- 2018
We consider the problem under what conditions the equation f″ + Af = 0 possesses an entire (meromorphic) solution with given sequences of zeros (poles) and critical points. The results are extended…
Solutions of complex differential equation having zeros on pre-given sequences
- Mathematics
- 2017
Behavior of solutions of f ′′ +Af = 0 is discussed under the assumption that A is analytic in D and sup z∈D (1 − |z|)|A(z)| < ∞, where D is the unit disc of the complex plane. As a main result it is…
Growth estimates for meromorphic solutions of higher order algebraic differential equations
- MathematicsTohoku Mathematical Journal
- 2020
We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is…
Solutions of Complex Differential Equation Having Pre-given Zeros in the Unit Disc
- Materials ScienceConstructive Approximation
- 2017
Behavior of solutions of f′′+Af=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…
Converse growth estimates for ODEs with slowly growing solutions
- Materials ScienceMathematische Zeitschrift
- 2020
Let f1,f2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…
References
SHOWING 1-10 OF 21 REFERENCES
Mean growth and geometric zero distribution of solutions of linear differential equations
- Mathematics
- 2014
The aim of this paper is to consider certain conditions on the coefficient A of the differential equation f″ + Af = 0 in the unit disc which place all normal solutions f in the union of Hardy spaces…
Normal families and linear differential equations
- Mathematics
- 2012
The aim of this paper is to provide a quantitative version of a normality criterion recently given by Grahl and Nevo [GN] and a new proof of it based on the Schwarzian derivative and associated…
Locally univalent functions in the unit disk
- Mathematics
- 1983
Hille [5] has shown that this theorem is sharp. Later on, Ahlfors and Weill [] proved that J' extends continuously (with respect to the spherical metric) to the boundary, provided k<1; in fact, they…
Ordinary Differential Equations In The Complex Domain
- Mathematics
- 2016
Thank you very much for reading ordinary differential equations in the complex domain, maybe you have knowledge that, people have look hundreds of times for their chosen readings like this, but end up in infectious downloads.
Bloch and normal functions and their relation
- Mathematics
- 1989
Following a brief introduction to Bloch and normal functions, several conditions, including a convergence theorem, are shown for determining them. In addition, since an exponential of any constant…
Boundary behaviour and normal meromorphic functions
- Mathematics, Philosophy
- 1957
t . This paper deals with the boundary behaviour of meromorphic functions. The considerations lead in a natural manner to a conformally invariant class of meromorphic functions, distinguished by a…
Properties of meromorphic φ-normal functions
- Mathematics
- 2011
Let M(D) denote the set of all meromorphic functions in the unit disc D := {z : |z| < 1} of the complex plane C, and let T stand for the set of all conformal self maps of D. The class N of normal…
New Findings on the Bank–Sauer Approach in Oscillation Theory
- Mathematics
- 2012
In 1988, S. Bank showed that if {zn} is a sparse sequence in the complex plane, with convergence exponent zero, then there exists a transcendental entire A(z) of order zero such that f″+A(z)f=0…
Univalent functions and Teichm?uller space
- Mathematics
- 1986
I Quasiconformal Mappings.- to Chapter I.- 1. Conformal Invariants.- 1.1 Hyperbolic metric.- 1.2 Module of a quadrilateral.- 1.3 Length-area method.- 1.4 Rengel's inequality.- 1.5 Module of a ring…