TY - JOUR

T1 - On the Robust Stability of Stationary Solutions to a Class of Mathieu-Type Equations

AU - Demidenko, G. V.

AU - Myagkikh, K. S.

N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008). Публикация для корректировки.

PY - 2023/3

Y1 - 2023/3

N2 - We consider a class of nonlinear ordinary differential equations of the second order with parameters. We establish conditions for perturbations of the coefficients of the equations under which the zero solution is asymptotically stable. Estimates for attraction sets of the zero solution and estimates of the stabilization rate of solutions at infinity are obtained. Using these results, theorems on the robust stability of stationary solutions are proven.

AB - We consider a class of nonlinear ordinary differential equations of the second order with parameters. We establish conditions for perturbations of the coefficients of the equations under which the zero solution is asymptotically stable. Estimates for attraction sets of the zero solution and estimates of the stabilization rate of solutions at infinity are obtained. Using these results, theorems on the robust stability of stationary solutions are proven.

KW - Mathieu-type equations

KW - asymptotic stability

KW - attraction sets

KW - estimates for solutions

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85163008464&origin=inward&txGid=e2f5d9920cbe134001fa165cf598b7a4

UR - https://www.mendeley.com/catalogue/ecaf0190-49d6-36a4-ab6a-0f429b7c975d/

U2 - 10.1134/S1995080223030113

DO - 10.1134/S1995080223030113

M3 - Article

VL - 44

SP - 883

EP - 895

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 3

ER -