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2005, Volume 2005: 624-633. Doi: 10.3934/proc.2005.2005.624 open access
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Geometric approach to a singular boundary value problem with turning points

  • 1.

    Department of Mathematics, University of Kansas, Lawrence, KS 66045

Received:  August 31, 2004
Revised:  April 30, 2005
Published:  August 2005
Abstract Related Papers Cited by
    Abstract
  • The singularly perturbed boundary value problem $\epsilon \ddot x=f(x,t;\epsilon)\dot x$, $x(-1;\epsilon)=A$, $x(0;\epsilon)=B$ is studied as an application of the geometric singular perturbation theory for turning points. The key ingredients are: the delay of stability loss that characterizes all possible singular orbits of the boundary value problem, and the exchange lemmas for problems with turning points as the geometric tool to show the existence of solutions shadowing singular orbits.
    Mathematics Subject Classification: Primary: 34E20; Secondary: 34B16.

    Citation:
    shu

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