International Journal of Differential Equations
Volume 2009 (2009), Article ID 373851, 16 pages
Research Article

Global Bifurcation for Second-Order Neumann Problem with a Set-Valued Term

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 17 September 2009; Accepted 3 November 2009

Academic Editor: Qingkai Kong

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.


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.