Boundary Value Problems
Volume 2008 (2008), Article ID 254593, 10 pages
doi:10.1155/2008/254593

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

Abstract

We consider the nonlinear eigenvalue problems u″+rf(u)=0, 0<t<1, u(0)=0, u(1)=∑i=1m−2αiu(ηi), where m≥3, ηi∈(0,1), and αi>0 for i=1,…,m−2, with ∑i=1m−2αi<1; r∈ℝ; f∈C1(ℝ,ℝ). There exist two constants s2<0<s1 such that f(s1)=f(s2)=f(0)=0 and f0:=limu→0(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.