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.