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

[摘要] 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 Neumann-Cauchy or a Neumann-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 degenerate 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 degenerate stable solution for sufficiently small epsilon and determine its asymptotic behavior in epsilon. (C) 1999 Academic Press.

[发布日期] 1999-12-10

[关键词] exchange of stabilities;singularly perturbed boundary value problems