Nonexistence and existence of positive solutions for 2nth-order singular superlinear problems with Strum-Liouville boundary conditions

This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C2n−2[0,1] positive solutions, and a sufficient condition, a necessary condition for the existence of C2n−1[0,1] positive solutions. Relations between the positive solutions and the Green's functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.