Differential Equations and Computational Simulations III
Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 109-117.

A bifurcation result for Sturm-Liouville problems with a set-valued term

Georg Hetzer

Abstract:
It is established in this note that
$$-(ku')'+g(\cdot,u)\in \mu F(\cdot,u)\,,$$ $u'(0)=0$, $u'(1)=0$
has a multiple bifurcation point at $(0,{\bf 0})$ in the sense that infinitely many continua meet at $ (0,{\bf 0})$. $F$ is a ``set-valued representation'' of a function with jump discontinuities along the line segment $[0,1]\times\{0\}$. The proof relies on a Sturm-Liouville version of Rabinowitz's bifurcation theorem and an approximation procedure.

Published November 12, 1998.
Mathematics Subject Classification: 34B15, 34C23, 47H04, 86A10.
Key words and phrases: Differential inclusion, Sturm-Liouville problem, Rabinowitz bifurcation.

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Georg Hetzer
Department of Mathematics, Auburn University
Auburn, AL 36849-5310, USA
E-mail address: hetzege@mail.auburn.edu
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