Electron. J. Diff. Equ., Vol. 2012 (2012), No. 214, pp. 1-13.

Direction of bifurcation for some non-autonomous problems

Philip Korman

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
email: kormanp@math.uc.edu

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