A complete description of continuous on the real line solutions of the linear functional equation of the second order with constant coefficients
Abstract
The paper provides an existence criterion and a complete description of continuos solutions f : R → R of the linear second-order functional equation f(f(x))+a f(x)+bx = 0 with constant coefficients.
Keywords
linear functional equation,
trajectory approach,
one-dimensional dynamics,
linear recurrent sequences
Supporting agencies: The work was performed at the Institute of Mathematics of the National Academy of Sciences of Belarus on assignment 1.2.01 "Development of constructive and asymptotic methods for the study of complex controlled differential and discrete systems" GPNI Convergence-2025" (subprogram "Mathematical models and methods")
About the Authors
M. V. Karpuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
P. A. Khudziakova
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
References
1. Milnor J. W. Dynamics in one complex variable: introductory lectures. doi: 10.48550/arXiv.math/9201272
2. Encyclopaedia of Mathematics. In 5 vol. Vol. 5. Moscow, Sovetskaya entsiklopediya, 1985. 1248 p. (in Russian).
3. Pelukh G. P., Sharkovsky A. N. Introduction to the theory of functional equations. Kyiv, Naukova Dumka, 1974. 120 p. (in Russian).
4. Antonevich A. B. Linear Functional Equations. Operator Approach. Birkhauser, 1996.
5. Markushevich A. I. Recurrent sequences. Moscow, Nauka, 1983. 48 p. (in Russian).
Review
For citations:
Karpuk M.V., Khudziakova P.A. 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. 2024;32(1):74-85. (In Russ.)
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