Electronic Journal of Differential Equations,
Conference 01 (1998), pp. 109-117

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

Authors: Georg Hetzer (Auburn Univ., Auburn, AL, USA)

 
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,{\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.
Math Subject Classifications: 34B15, 34C23, 47H04, 86A10.
Key Words: Differential inclusion; Sturm-Liouville problem; Rabinowitz bifurcation.