Nonlinear Differential Equations,
Electron. J. Diff. Eqns., Conf. 05, 2000, pp. 311-322.

Instability and exact multiplicity of solutions of semilinear equations

Philip Korman & Junping Shi

Abstract:
For a class of two-point boundary-value problems we use bifurcation theory to show that a solution is unstable under a simple, geometric in nature, assumption on the non-linear term. As an application we obtain some new exact multiplicity results.

Published October 31, 2000.
Math Subject Classifications: 34B15.
Key Words: Bifurcation of solutions, global solution curve.

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Philip Korman
Institute for Dynamics and
Department of Mathematical Sciences
University of Cincinnati
Cincinnati Ohio 45221-0025
e-mail: kormanp@math.uc.edu

Junping Shi
Department of Mathematics, College of William and Mary
Williamsburg, VA 23187, USA
And: Department of Mathematics
Tulane University
New Orleans, LA 70118 USA
e-mail: jxshix@facstaff.wm.edu

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