Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term

By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation , with and , where denotes the linear operator , and . This equation is viewed as a perturbation of the fourth-order Sturm-Liouville problem, where the perturbed term only satisfies the global Caratheodory conditions, which implies that the perturbed effect of on is quite large so that the nonlinearity can tend to negative infinity at some singular points.