Bounded solutions of a second order difference equation with jumps of operator coefficient

Authors

DOI:

https://doi.org/10.17721/1812-5409.2022/2.7

Keywords:

Difference equation, bounded solution, Banach space

Abstract

We study the problem of existence of a unique bounded solution of a difference equation of the second order with a variable operator coefficient in a Banach space. In the case of a finite number of jumps of an operator coefficient necessary and sufficient conditions are obtained.

Pages of the article in the issue: 57 - 61

Language of the article: English

References

HENRY, D. (1981) Geometric Theory of Semilinear Parabolic Equations. Berlin: Springer.

RISS F. and SEKEFAL’VI NAD’ (1996) Lectures on functional analysis. Moscow: Mir.

GONCHAR, I. (2016) On the bounded solutions of a difference equation with a jump of an operator coefficient. Bulletin of Taras Shevchenko National University of Kyiv. Series Physics & Mathematics. 2. p. 25-28.

GORODNII, M. & GONCHAR, I. (2016) On the bounded solutions of a difference equation with variable operator coefficient. Reports of the National Academy of Sciences of Ukraine 12. p. 12-16.

CHAIKOVS’KYI, A. & LAGODA, O. (2020) Bounded solutions of a difference equation with finite number of jumps of operator coefficient. Carpathian Mathematical Publications 12(1). p. 165-172.

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Published

2022-10-12

How to Cite

Chaikovs’kyi, A., & Lagoda, O. (2022). Bounded solutions of a second order difference equation with jumps of operator coefficient. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (2), 57–61. https://doi.org/10.17721/1812-5409.2022/2.7

Issue

Section

Differential equations, mathematical physics and mechanics