Oleksandr Liubimov

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math.DS2025

Boundedness of solutions of the first-order linear multidimensional difference equations

Andrii Chaikovskyi, Oleksandr Liubimov

We investigate the boundedness of solutions of the first order linear difference equation of the form $x_{n + 1} = A x_{n} + y_{n}, n \geq 1$ where $A$ is a square matrix with comp…

math.DS2025

Ergodic approach to the study of boundedness of solutions of one type of the first-order semilinear difference equations

Andrii Chaikovskyi, Oleksandr Liubimov

We investigate the sufficient conditions for boundedness of one type of difference equations of the form $x (n + 1) = a x (n) + f (x (n)) + y (n), n \geq 1$ in critical case $∣ a ∣ = 1$ . For this…