TY - JOUR

T1 - Теорема об области асимптотической устойчивости и её приложения

AU - Иванов, Геннадий Григорьевич

AU - Алферов, Геннадий Викторович

AU - Королев, Владимир Степанович

PY - 2022

Y1 - 2022

N2 - The article considers a theorem on the region of asymptotic stability of solutions of ordinary differential equations, which is generalized to the case of a system of equations, where the right-hand side explicitly depends on time. It is shown how it can be used to answer the question of whether the equation under consideration has periodic solutions other than the trivial one, and how, using the constructed Lyapunov functions, one can find these periodic solutions.

AB - The article considers a theorem on the region of asymptotic stability of solutions of ordinary differential equations, which is generalized to the case of a system of equations, where the right-hand side explicitly depends on time. It is shown how it can be used to answer the question of whether the equation under consideration has periodic solutions other than the trivial one, and how, using the constructed Lyapunov functions, one can find these periodic solutions.

UR - https://www.mendeley.com/catalogue/63f70558-1fda-3e70-a6af-3ae9bce7097f/

U2 - 10.17072/1993-0550-2022-1-5-13

DO - 10.17072/1993-0550-2022-1-5-13

M3 - статья

VL - 56

SP - 5

EP - 13

JO - ВЕСТНИК ПЕРМСКОГО УНИВЕРСИТЕТА. СЕРИЯ: МАТЕМАТИКА. МЕХАНИКА. ИНФОРМАТИКА

JF - ВЕСТНИК ПЕРМСКОГО УНИВЕРСИТЕТА. СЕРИЯ: МАТЕМАТИКА. МЕХАНИКА. ИНФОРМАТИКА

SN - 1993-0550

IS - 1(56)

ER -