2005, 2005(Special): 624-633. doi: 10.3934/proc.2005.2005.624

Geometric approach to a singular boundary value problem with turning points

1. 

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

Received  September 2004 Revised  May 2005 Published  September 2005

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.
Citation: Weishi Liu. Geometric approach to a singular boundary value problem with turning points. Conference Publications, 2005, 2005 (Special) : 624-633. doi: 10.3934/proc.2005.2005.624
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