On properties of the solutions of the Weber equation

Trukhan, Yu.S.

doi:10.15330/cmp.7.2.247-253

Cited by 2 publications

(1 citation statement)

References 2 publications

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“…Entire functions of bounded index have been used in the theory of value distribution and differential equations [2,4,8,11,[14][15][16]. A full bibliography can be found in [6].…”

Section: Introductionmentioning

confidence: 99%

Boundedness of the L-index in a direction of entire solutions of second order partial differential equation

Bandura

Скасків

2019

ACUTM

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We construct a continuous function L : C 2 → (0, +∞) 2 such that every entire solution of a certain second order partial differential equation has bounded L-index in a direction b = (b1, b2) ∈ C 2 \ {0}. On the other hand, the entire bivariate function F (z1, z2) = cos √ z1z2 is a solution of this equation. The function F has unbounded index in each direction b ∈ C 2 \ {0}. The constructed function L is a full solution of a problem posed by A. A. Kondratyuk's in 2007 about the existence of the function L with specified properties. We also suggest a continuous function L1 : C 2 → (0, +∞) 2 such that the function F has bounded L1-index in every direction b ∈ C n \ {0}.

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“…Entire functions of bounded index have been used in the theory of value distribution and differential equations [2,4,8,11,[14][15][16]. A full bibliography can be found in [6].…”

Section: Introductionmentioning

confidence: 99%

Boundedness of the L-index in a direction of entire solutions of second order partial differential equation

Bandura

Скасків

2019

ACUTM

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Boundedness of L-index in joint variables for composition of analytic functions in the unit ball

Bandura

2020

Asian-European J. Math.

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In this paper, the following composite analytic functions [Formula: see text] and [Formula: see text] are considered, where [Formula: see text] [Formula: see text] [Formula: see text] We established conditions which provide equivalence of boundedness of the [Formula: see text]-index of the function [Formula: see text] and boundedness of the [Formula: see text]-index in joint variables of the function [Formula: see text] where [Formula: see text] is a continuous function, [Formula: see text] [Formula: see text] For the function [Formula: see text] with additional restrictions, the function [Formula: see text] is constructed such that [Formula: see text] has bounded [Formula: see text]-index in joint variables in the case when the function [Formula: see text] has bounded [Formula: see text]-index in the direction [Formula: see text], where [Formula: see text] is a positive continuous function. Our proofs are based on the application of analog of Hayman’s theorem for these classes of functions.

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On properties of the solutions of the Weber equation

Abstract: Growth, convexity and the l-index boundedness of the functions α(z) and β(z), such that α(z 4 ) and zβ(z 4 ) are linear independent solutions of the Weber equation w ′′ − (

Cited by 2 publications

References 2 publications

Boundedness of the L-index in a direction of entire solutions of second order partial differential equation

Boundedness of the L-index in a direction of entire solutions of second order partial differential equation

Boundedness of L-index in joint variables for composition of analytic functions in the unit ball

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