2. Articole

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Author: search.filters.author.Cheban, DavidStart date: 2020

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    POISSON STABLE MOTIONS OF MONOTONE AND STRONGLY SUB-LINEAR NON-AUTONOMOUS DYNAMICAL SYSTEMS
    (Hybrid & Monthly, 2023) Cheban, David
    This paper is dedicated to the study of the problem of existence of Poisson stable (Bohr/Levitan almost periodic, almost automorphic, almost recurrent, recurrent, pseudo periodic, pseudo recurrent and Poisson stable) motions of monotone sub-linear non-autonomous dynamical systems. The main results we establish in the framework of general non-autonomous (cocycle) dynamical systems. We apply our general results to the study of the problem of existence of different classes Poisson stable solutions of some types of non-autonomous evolutionary equations (Ordinary Differential Equations, Functional-Differential Equations with finite delay and Difference Equations).
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    AVERAGING PRINCIPLE ON SEMI-AXIS FOR SEMI-LINEAR DIFFERENTIAL EQUATIONS
    (Casa Editorial-Poligrafică „Bons Offices”, 2022) Cheban, David
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    AVERAGING PRINCIPLE ON INFINITE INTERVALS FOR STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS
    (AIMS Press, 2021) Cheban, David; Zhenxin, Liu
    In contrast to existing works on stochastic averaging on finite intervals, we establish an averaging principle on the whole real axis, i.e. the so-called second Bogolyubov theorem, for semilinear stochastic ordinary differential equations in Hilbert space with Poisson stable (in particular, periodic, quasi-periodic, almost periodic, almost automorphic etc) coefficients. Under some appropriate conditions we prove that there exists a unique recurrent solution to the original equation, which possesses the same recurrence property as the coefficients, in a small neighborhood of the stationary solution to the averaged equation, and this recurrent solution converges to the stationary solution of averaged equation uniformly on the whole real axis when the time scale approaches zero.
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    NON-AUTONOMOUS DYNAMICAL SYSTEMS AND THEIR APPLICATIONS
    (Academia de Ştiinţe a Moldovei, 2021) Cheban, David
    Articolul reprezintă o scurtă trecere în revistă a cercetărilor efectuate de autor în ultimii 10-15 ani privind sistemele dinamice neautonome şi aplicațiile acestora. Sistemele dinamice neautonome constituie un nou domeniu ce contribuie la dezvoltarea rapidă a matematicii (teoria sistemelor dinamice). Mii de articole, inclusiv zeci de articole de sinteză și un șir de monografii despre sistemele dinamice neautonome au fost publicate în ultimele decenii, iar problematica respectivă a făcut cap de afiș la conferințele internaționale. Autorul a publicat trei monografii pe problema sistemelor dinamice neautonome. În acest articol este oferită o prezentare generală a rezultatelor obținute.
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    ALMOST PERIODIC AND ALMOST AUTOMORPHIC SOLUTIONS OF MONOTONE DIFFERENTIAL EQUATIONS WITH A STRICT MONOTONE FIRST INTEGRAL
    (Institutul de Matematică şi Informatică al AŞM, 2020) Cheban, David
    The paper is dedicated to the study of problem of Poisson stability (in particular periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, Levitan almost periodicity, pseudo-periodicity, almost recurrence in the sense of Bebutov, recurrence in the sense of Birkhoff, pseudo-recurrence, Poisson stability) and asymptotical Poisson stability of motions of monotone non-autonomous differential equations which admit a strict monotone first integral. This problem is solved in the framework of general non-autonomous dynamical systems.