NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH STRUM-LIOUVILLE BOUNDARY CONDITIONS

摘要

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.