Publication result detail

NEW CONDITIONS FOR EXISTENCE OF THE SOLUTION TO THE DISCRETE EMDEN-FOWLER TYPE EQUATION WITH POWER ASYMPTOTICS

DIBLÍK, J.; KOROBKO, E.

Original Title

NEW CONDITIONS FOR EXISTENCE OF THE SOLUTION TO THE DISCRETE EMDEN-FOWLER TYPE EQUATION WITH POWER ASYMPTOTICS

English Title

NEW CONDITIONS FOR EXISTENCE OF THE SOLUTION TO THE DISCRETE EMDEN-FOWLER TYPE EQUATION WITH POWER ASYMPTOTICS

Type

Paper in proceedings outside WoS and Scopus

Original Abstract

In the paper, we continue research on the existence of solutions with power-type asymptotics to the following discrete Emden-Fowler type equation $$\Delta^2 u(k)= k^\alpha u^m(k) = 0;$$ where $k \ge k_0$, k is an independent variable, $k_0$ is a fixed integer, $u: \{k_0; k_0 + 1; ...\} \to \mathbb{R}$, $\Delta u(k)$, $\Delta^2u(k)$ are the first and second-order differences of $u(k)$ respectively and $m$ and $\alpha$ are real numbers. As a result, the present paper gives new conditions for the values $m$ and $\alpha$ guaranteeing the existence of solutions with power-type asymptotics. The results are compared with those previously known and visualized in the $(m; \alpha)$-plane.

English abstract

In the paper, we continue research on the existence of solutions with power-type asymptotics to the following discrete Emden-Fowler type equation $$\Delta^2 u(k)= k^\alpha u^m(k) = 0;$$ where $k \ge k_0$, k is an independent variable, $k_0$ is a fixed integer, $u: \{k_0; k_0 + 1; ...\} \to \mathbb{R}$, $\Delta u(k)$, $\Delta^2u(k)$ are the first and second-order differences of $u(k)$ respectively and $m$ and $\alpha$ are real numbers. As a result, the present paper gives new conditions for the values $m$ and $\alpha$ guaranteeing the existence of solutions with power-type asymptotics. The results are compared with those previously known and visualized in the $(m; \alpha)$-plane.

Keywords

Emden-Fowler equation, discrete equation, nonlinear equation, asymptotic behaviour.

Key words in English

Emden-Fowler equation, discrete equation, nonlinear equation, asymptotic behaviour.

Authors

DIBLÍK, J.; KOROBKO, E.

RIV year

2022

Released

16.06.2022

Publisher

UNOB Brno

Location

Brno

ISBN

978-80-7582-456-1

Book

Mathematics, Information Technologies and Applied Sciences 2022, post-conference proceedings

Pages from

1

Pages to

11

Pages count

11

URL

https://mitav.unob.cz/index.html

BibTex

@inproceedings{BUT178265,
  author="Josef {Diblík} and Evgeniya {Korobko}",
  title="NEW CONDITIONS FOR EXISTENCE OF THE SOLUTION TO THE DISCRETE EMDEN-FOWLER TYPE EQUATION WITH POWER ASYMPTOTICS",
  booktitle="Mathematics, Information Technologies  and Applied Sciences 2022,  post-conference proceedings",
  year="2022",
  pages="1--11",
  publisher="UNOB Brno",
  address="Brno",
  isbn="978-80-7582-456-1",
  url="https://mitav.unob.cz/index.html"
}