Asymptotic behavior of solutions of a second-order nonlinear discrete equation of Emden-Fowler type

The article investigates a second-order nonlinear difference equation of Emden-Fowler type. New conditions with respect to parameters of equation are found such that the equation admits a solution asymptotically represented by a power function that is asymptotically equivalent to the exact solution of the nonlinear second-order differential Emden-Fowler equation. Two-term asymptotic representations are given not only for the solution itself but also for its first- and second-order forward diffrences as well. Previously known results are discussed, and illustrative examples are considered.

Keywords

Discrete equation, Emden-Fowler equation, equation of the second-order, asymptotic behavior, nonlinearity

Citation

Advances in Nonlinear Analysis. 2023, vol. 12, issue 1, p. 1-23.
https://www.degruyter.com/document/doi/10.1515/anona-2023-0105/html

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence

Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/