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Proceedings of the Institute of Mathematics of the NAS of Belarus, 2024, Volume 32, Number 1, Pages 74–85 (Mi timb385)  
DIFFERENTIAL EQUATIONS, DYNAMIC SYSTEMS AND OPTIMAL CONTROL

A complete description of continuous on the real line solutions of the linear functional equation of the second order with constant coefficients

M. V. Karpuk, P. A. Khudziakova

Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk, Belarus
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Abstract: The paper provides an existence criterion and a complete description of continuos solutions $f\colon\mathbb R\to \mathbb R$ of the linear second-order functional equation $f(f(x))+af(x)+bx=0$ with constant coefficients.
Keywords: linear functional equation, trajectory approach, one-dimensional dynamics, linear recurrent sequences.
Funding agency Grant number
ГПНИ "Конвергенция-2025"
Received: 25.03.2024
Revised: 07.06.2024
Accepted: 18.06.2024
Document Type: Article
UDC: 517.965
Language: Russian
Citation: M. V. Karpuk, P. A. Khudziakova, “A complete description of continuous on the real line solutions of the linear functional equation of the second order with constant coefficients”, Proceedings of the Institute of Mathematics of the NAS of Belarus, 32:1 (2024), 74–85
Citation in format AMSBIB
\Bibitem{KarKhu24}
\by M.~V.~Karpuk, P.~A.~Khudziakova
\paper A complete description of continuous on the real line solutions of the linear functional equation of the second order with constant coefficients
\jour Proceedings of the Institute of Mathematics of the NAS of Belarus
\yr 2024
\vol 32
\issue 1
\pages 74--85
\mathnet{http://mi.mathnet.ru/timb385}
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