IJPAM: Volume 78, No. 4 (2012)
A SUPPLEMENT TO POINCARÉ'S THEOREM
ON DIFFERENCE EQUATIONS
ON DIFFERENCE EQUATIONS
Victor Adukov
Department of Differential Equations and Dynamical Systems
South Ural State University
Chelyabinsk, 454080, RUSSIAN FEDERATION
Department of Differential Equations and Dynamical Systems
South Ural State University
Chelyabinsk, 454080, RUSSIAN FEDERATION
Abstract. The second-order linear difference equation of Poincaré type

with Buslaev's restrictions on coefficients
![\begin{displaymath}
\limsup\limits_{n\to\infty}\sqrt[n]{\vert\alpha(n)\vert}\le...
...limsup\limits_{n\to\infty}\sqrt[n]{\vert\beta(n)\vert}\le q<1
\end{displaymath}](img2.png)
is considered. It is assumed that the characteristic roots of the equation have the same modulus. The set


Received: June 9, 2012
AMS Subject Classification: 39A10
Key Words and Phrases: second-order difference equation of Poincaré type, Poincaré's theorem, asymptotic behavior, Padé approximants
Download paper from here.
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 4