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

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.

Keywords

• Differential inclusion
• Sturm-Liouville problem
• Rabinowitz bifurcation.