Multiple Solutions for Nonlinear Doubly Singular Three-Point Boundary Value Problems with Derivative Dependence

We study the existence of multiple nonnegative solutions for the doubly singular three-point boundary value problem with derivative dependent data function ？(()′())′=()(,(),()′()),0<<1,(0)=0,(1)=1(). Here, ∈[0,1]∩1(0,1] with ()>0 on (0,1] and () is allowed to be discontinuous at =0. The fixed point theory in a cone is applied to achieve new and more general results for existence of multiple nonnegative solutions of the problem. The results are illustrated through examples.