Boundary Value Problems
Volume 2011 (2011), Article ID 715836, 12 pages
Research Article

Global Structure of Nodal Solutions for Second-Order m-Point Boundary Value Problems with Superlinear Nonlinearities

Department of Mathematics, Shanghai Institute of Technology, Shanghai 200235, China

Received 8 May 2010; Revised 1 August 2010; Accepted 23 September 2010

Academic Editor: Feliz Manuel Minhós

Copyright © 2011 Yulian An. 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 consider the nonlinear eigenvalue problems u+λf(u)=0, 0<t<1, u(0)=0, u(1)=i=1m-2αiu(ηi), where m3, ηi(0,1), and αi>0 for i=1,,m-2, with i=1m-2αi<1, and fC1(\{0},)C(,) satisfies f(s)s>0 for s0, and f0=, where f0=lim|s|0f(s)/s. We investigate the global structure of nodal solutions by using the Rabinowitz's global bifurcation theorem.