Turkish Journal of Mathematics
DOI
10.3906/mat-1904-30
Abstract
In this paper we investigate the Volterra difference equation of the form $ \D(r_n\D x_n)=b_n+\sum_{k=1}^{n}K(n,k)f(x_k). $ We establish sufficient conditions for the existence of a solution $x$ of the above equation with the property $ x_n=y_n+\o(n^s), $ where $y$ is a given solution of the equation $\D(r_n\D y_n)=b_n$ and $s$ is nonpositive real number. We also obtain sufficient conditions for the existence of asymptotically periodic solutions.
Keywords
Volterra difference equation, quasidifference, asymptotic behavior, asymptotically periodic solution, convergent solution
First Page
2203
Last Page
2217
Recommended Citation
MIGDA, MALGORZATA and DUTKIEWICZ, ALDONA
(2019)
"Asymptotic behavior of solutions of second-order difference equations of Volterra type,"
Turkish Journal of Mathematics: Vol. 43:
No.
5, Article 12.
https://doi.org/10.3906/mat-1904-30
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss5/12
