Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 03, pp. 1-10.

Title: Bifurcation from intervals for Sturm-Liouville problems and its applications

Authors: Guowei Dai (Northwest Normal Univ., Lanzhou, China)
         Ruyun Ma   (Northwest Normal Univ., Lanzhou, China)

Abstract:
 We study the unilateral global bifurcation for the nonlinear
 Sturm-Liouville problem
 $$\displaylines{
 -(pu')'+qu=\lambda au+af(x,u,u',\lambda)+g(x,u,u',\lambda)\quad x\in(0,1),\cr
 b_0u(0)+c_0u'(0)=0,\quad b_1u(1)+c_1u'(1)=0,
 }$$
 where $a\in C([0, 1], [0,+\infty))$ and $a(x)\not\equiv 0$ on any subinterval
 of $[0, 1]$, $f,g\in C([0,1]\times\mathbb{R}^3,\mathbb{R})$ and f is
 not necessarily differentiable at the origin or infinity with respect to u.
 Some applications are given to nonlinear second-order two-point boundary-value
 problems. This article is a continuation of [8].
 
Submitted September 8, 2013. Published January 03, 2014.
Math Subject Classifications: 34B24, 34C10, 34C23.
Key Words: Global bifurcation; nodal solutions; eigenvalues.