We study the exact multiplicity of positive solutions, and the global solution structure for several classes of non-autonomous two-point problems. We present two situations where the direction of turn can be computed rather directly. As an application, we consider a problem from combustion theory with a sign-changing potential. We illustrate our results by numerical computations, using a novel method.
Submitted June 28, 2012. Published November 27, 2012.
Math Subject Classifications: 34B15, 65L10, 80A25.
Key Words: Global solution curves; direction of bifurcation; continuation in a global parameter.
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| Philip Korman |
Department of Mathematical Sciences
University of Cincinnati
Cincinnati, Ohio 45221-0025, USA
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