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Geometric approach to a singular boundary value problem with turning points

Pages: 624 - 633, Issue Special, August 2005

 Abstract        Full Text (180.7K)              

Weishi Liu - Department of Mathematics, University of Kansas, Lawrence, KS 66045, United States (email)

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.

Keywords:  Turning points, Delay of stability loss, Exchange Lemmas.
Mathematics Subject Classification:  Primary: 34E20; Secondary: 34B16.

Received: September 2004;      Revised: May 2005;      Published: September 2005.