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