Singularly Perturbed Boundary Value Problems for Systems of Tichonov's Type in Case of Exchange of Stabilities
نویسندگان
چکیده
We consider a system of ordinary di erential equations consisting of a singularly perturbed scalar di erential equation of second order and a scalar di erential equation of rst 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 su ciently small " and determine its asymptotic behavior in ".
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