Sufficient conditions for the existence of the solution of an infinite-difference equation with variable coefficients
https://doi.org/10.22405/2226-8383-2024-25-2-243-250
Abstract
The paper discusses a difference equation of the form
Σ︀𝑟𝑙=0 𝑎𝑘,𝑙𝑍𝑘+𝑙 = 𝑦𝑘 (𝑘 ∈ Z), where 𝑟 ∈ N, 𝑦 = {𝑦𝑘}𝑘∈Z is a given numerical sequence from the space 𝑙𝑝 (1 ⩽ 𝑝 < ∞), provided that the matrix 𝐴 = (𝑎𝑘,𝑙), 𝑎𝑘,𝑙 ∈ 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 𝑎𝑘,𝑙, at which the equation has a unique solution 𝑍 = {𝑍𝑘}𝑘∈Z, belonging to the space 𝑙_𝑝. For the norm of this solution, a numerical estimate is given from above.
About the Authors
Sergei Ernestovich Nohrin
Krasovskii Institute of Mathematics and Mechanics (Ural Branch) of the RAS
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Valerii Trifonovich Shevaldin
Krasovskii Institute of Mathematics and Mechanics (Ural Branch) of the RAS
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
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Review
For citations:
Nohrin S.E., Shevaldin V.T. Sufficient conditions for the existence of the solution of an infinite-difference equation with variable coefficients. Chebyshevskii Sbornik. 2024;25(2):243-250. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-2-243-250
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