Copyright © 2009 Ruyun Ma and Jiemei Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.