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DIBLÍK, J. KOROBKO, E.
Original Title
NEW CONDITIONS FOR EXISTENCE OF THE SOLUTION TO THE DISCRETE EMDEN-FOWLER TYPE EQUATION WITH POWER ASYMPTOTICS
Type
article in a collection out of WoS and Scopus
Language
English
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.
Keywords
Emden-Fowler equation, discrete equation, nonlinear equation, asymptotic behaviour.
Authors
DIBLÍK, J.; KOROBKO, E.
Released
16. 6. 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
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" }