Bifurcation from intervals for Sturm-Liouville problems and its applications

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].