WIAS Preprint No. 408, (1998)

Singularly perturbed boundary value problems for systems of Tichonov's type in case of exchange of stabilities


  • Butuzov, Valentin F.
  • Nefedov, Nikolai N.
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 34B15 34E20


  • exchange of stabilities, singularly perturbed boundary


We consider a system of ordinary differential equations consisting of a singularly perturbed scalar differential equation of second order and a scalar differential equation of first or second order and study a Neuman-Cauchy or a Neuman-Dirichlet problem. We assume that the degenerate equation has two intersecting solutions such that the standard theory for systems of Tichonov's type cannot be applied. We introduce the notation of a composed stable solution. By means of the technique of ordered lower and upper solutions we prove the existence of a solution of our problems near the composed stable solution for sufficiently small ε and determine its asymptotic behavior in ε.

Appeared in

  • J. Differential Equations, 159 (1999), No. 2, pp. 427-446

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