On the Stability of Integral Manifolds of a System of Ordinary Differential Equations in the Critical Case

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 262; no. 6; pp. 825 - 834
• Main Authors: Kuptsov, M. I., Minaev, V. A., Faddeev, A. O., Yablochnikov, S. L.
• Format: Journal Article
• Language: English
• Published: New York Springer US 16.04.2022; Springer; Springer Nature B.V
• Subjects: Differential equations; Fixed points (mathematics); Independent variables; Linear systems; Manifolds (mathematics); Mathematical analysis; Mathematics; Mathematics and Statistics; Operators (mathematics); Parameters; Stability; operator equation; 34C25; 34D35; method of transform matrices; 34C45; 34A34; Lyapunov method; stability of integral manifolds; system of ordinary differential equations

In this paper, we consider the stability problem for nonzero integral manifolds of a nonlinear, finite-dimensional system of ordinary differential equations whose right-hand side is a vector-valued function containing a parameter and periodic in an independent variable. We assume that the system pos...