More on the Asymptotic Behaviour of Solutions to a Second Order Emden-Fowler Difference Equation

conference paper

English

The paper investigates a second order difference equation of the Emden-Fowler type Lambda(2)u(k) +/- k(alpha)u(m)(k) = 0, where k is the independent variable taking values k = k(0), k(0) + 1,... with k(0) a fixed integer, u: {k(0), k(0) + 1, ...} -> R is the dependent variable and.2u(k) is its second-order forward difference. New conditions with respect to parameters m is an element of R, m not equal 1 and alpha is an element of R are found such that the equation admits a solution asymptotically represented by a power function asymptotically equivalent with the exact solution of second-order differential Emden-Fowler equation y ''(x) +/- x(alpha)y(m)(x) = 0.

Emden-Fowler discrete equation; power-type solution; difference system

DIBLÍK, J.; KOROBKO, E.

7. 6. 2024

AMER INST PHYSICS

MELVILLE

9780735449541

AIP Conference Proceedings, Volume 3094, Issue 1, 7 June 2024, International Conference of Numerical Analysis and Applied Mathematics 2022, ICNAAM 2022

0094-243X

AIP conference proceedings

3094

1

United States of America

400002-1

400002-4

4

https://pubs.aip.org/aip/acp/article/3094/1/400002/3297149/More-on-the-asymptotic-behaviour-of-solutions-to-a