Publication detail

# Dominant and subdominant positive solutions to generalized Dickman equation, Applied Mathematics and Computations

DIBLÍK, J. MEDINA, R.

Original Title

Dominant and subdominant positive solutions to generalized Dickman equation, Applied Mathematics and Computations

English Title

Dominant and subdominant positive solutions to generalized Dickman equation, Applied Mathematics and Computations

Type

journal article in Web of Science

Language

en

Original Abstract

The paper considers a generalized Dickman equation. It is proved that there are two mutually disjoint sets of positive decreasing solutions such that, for every two solutions from different sets, the limit of their ratio equals 0 or ∞. The asymptotic behavior of such solutions is derived and a structure formula utilizing such solutions and describing all the solutions of a given equation is discussed. In addition, a criterion is proved giving sufficient conditions for initial functions to generate solutions falling into the first or the second set. Illustrative examples are given. Some open problems are suggested to be solved.

English abstract

The paper considers a generalized Dickman equation. It is proved that there are two mutually disjoint sets of positive decreasing solutions such that, for every two solutions from different sets, the limit of their ratio equals 0 or ∞. The asymptotic behavior of such solutions is derived and a structure formula utilizing such solutions and describing all the solutions of a given equation is discussed. In addition, a criterion is proved giving sufficient conditions for initial functions to generate solutions falling into the first or the second set. Illustrative examples are given. Some open problems are suggested to be solved.

Keywords

Generalized Dickman equation; Positive solution; Dominant solution; Subdominant solution; Asymptotic behavior; Delay

Released

26.09.2018

ISBN

0096-3003

Periodical

APPLIED MATHEMATICS AND COMPUTATION

Year of study

2018

Number

320

State

US

Pages from

169

Pages to

186

Pages count

17

URL

Documents

BibTex

```
@article{BUT150428,
author="Josef {Diblík} and Rigoberto {Medina}",
title="Dominant and subdominant positive solutions to generalized Dickman equation,
Applied Mathematics and Computations",
annote="The paper considers a generalized Dickman equation. It is proved that there are two mutually disjoint sets of positive decreasing solutions such that, for every two solutions from different sets, the limit of their ratio equals 0 or ∞. The asymptotic behavior of such solutions is derived and a structure formula utilizing such solutions and describing all the solutions of a given equation is discussed. In addition, a criterion is proved giving sufficient conditions for initial functions to generate solutions falling into the first or the second set. Illustrative examples are given. Some open problems are suggested to be solved.
",
chapter="150428",
doi="10.1016/j.amc.2018.03.090",
howpublished="print",
number="320",
volume="2018",
year="2018",
month="september",
pages="169--186",
type="journal article in Web of Science"
}
```