• Media type: E-Book; Report; Text
  • Title: Singularly perturbed boundary value problems for systems of Tichonov's type in case of exchange of stabilities
  • Contributor: Butuzov, Valentin F. [Author]; Nefedov, Nikolai N. [Author]; Schneider, Klaus R. [Author]
  • imprint: Weierstrass Institute for Applied Analysis and Stochastics publication server, 1998
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.408
  • Keywords: 34B15 ; article ; 34E20 ; exchange of stabilities -- singularly perturbed boundary
  • Origination:
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  • Description: 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.