Singularly perturbed systems: Case of exchange of stability
- Nefedov, Nikolai
- Schneider, Klaus R.
2010 Mathematics Subject Classification
- 34D15 34E05
- Singular perturbation, asymptotic methods, exchange of stability, upper and lower solutions
We consider systems of singularly perturbed ordinary differential equations and study the initial value problem on a finite interval. Our goal is to describe the asymptotic behavior of its solution with respect to ε in case of exchange of stability of a solution of the degenerate system considered as a steady state solution of the associated system. The obtained results extend the well-known fundamental theorems due to A.N. Tikhonov and A.B. Vasil'eva.