Boundary Value Problems
Volume 2008 (2008), Article ID 254593, 10 pages
Research Article

Global Behavior of the Components for the Second Order m-Point Boundary Value Problems

Yulian An1,2 and Ruyun Ma1

1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 9 October 2007; Accepted 16 December 2007

Academic Editor: Kanishka Perera

Copyright © 2008 Yulian An and Ruyun Ma. 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+rf(u)=0, 0<t<1, u(0)=0, u(1)=i=1m2αiu(ηi), where m3, ηi(0,1), and αi>0 for i=1,,m2, with i=1m2αi<1; r; fC1(,). There exist two constants s2<0<s1 such that f(s1)=f(s2)=f(0)=0 and f0:=limu0(f(u)/u)(0,), f:=lim|u|(f(u)/u)(0,). Using the global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above problems.