Geodesic
Sufficient conditions for the existence of the solution of an infinite-difference equation with variable coefficients
Čebyševskij sbornik, Tome 25 (2024) no. 2, pp. 243-250

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The paper discusses a difference equation of the form $\sum_{l=0}^{r}a_{k,l}Z_{k+l}=y_{k}\ (k\in \mathbb{Z})$, where $r\in \mathbb{N},\ y=\{y_k\}_{k\in \mathbb{Z}}$ is a given numerical sequence from the space ${{l}_{p}}\ (1\le p\infty)$, provided that the matrix $A=(a_{k,l})$, $a_{k,l}\in \mathbb{R}$, satisfies some condition close to the presence of a dominant diagonal. With the help of the fixed point theorem, sufficient conditions are written for the coefficients $a_{k,l}$, at which the equation has a unique solution $Z=\{ Z_{k}\}_{k\in \mathbb{Z}}$, belonging to the space $l_p$. For the norm of this solution, a numerical estimate is given from above.
Keywords: difference equation, sequences, space $l_p$, solution norm. 
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     author = {S. E. Nohrin and V. T. Shevaldin},
     title = {Sufficient conditions for the existence of the solution of an infinite-difference equation with variable coefficients},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {243--250},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a14/}
}
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S. E. Nohrin; V. T. Shevaldin. Sufficient conditions for the existence of the solution of an infinite-difference equation with variable coefficients. Čebyševskij sbornik, Tome 25 (2024) no. 2, pp. 243-250. http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a14/