... Necessary and Sufficient Condition for Existence of Positive Solutions In this section, by using the fixed point theorem of cone, we establish the following necessary and sufficient condition for the ... derivative of the unknown function u, and the second one isthat the nonlinearity ft, u, v, w may be singular at u, v, t 0and/ ort 1. In this paper, we study the existence of positive solutions and ... of Positive Solutions to a Class of SingularElastic Beam EquationsHuiqin LuSchool of Mathematical Sciences, Shandong Normal University , Jinan, 250014 Shandong, ChinaCorrespondence should be...