WIAS Preprint No. 158, (1995)

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.

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