global bifurcation for second-order neumann problem with a set-valued term

Abstract

We study the global bifurcation of the differential inclusion of the form −(ku′)′+g(⋅,u)∈μF(⋅,u),  u′(0)=0=u′(1), where F is a “set-valued representation” of a function with jump discontinuities along the line segment [0,1]×{0}. The proof relies on a Sturm-Liouville version of Rabinowitz's bifurcation theorem and an approximation procedure.