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

By Georg Hetzer

Abstract

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

Topics: Differential inclusion, Sturm-Liouville problem, Rabinowitz bifurcation., Mathematics, QA1-939, Science, Q, DOAJ:Mathematics, DOAJ:Mathematics and Statistics
Publisher: Texas State University
Year: 1998
OAI identifier: oai:doaj.org/article:05eb9bbbaee14453a0ea5951a0597b02
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