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.

Abstract

We consider the nonlinear eigenvalue problems u″+λf(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, and f∈C1(ℝ\{0},ℝ)∩C(ℝ,ℝ) satisfies f(s)s>0 for s≠0, 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.