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NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH STRUM-LIOUVILLE BOUNDARY CONDITIONS
Authors:Zhao Zengqin School of Mathematical Sciences  Qufu Normal University  Qufu  China
Institution:Zhao Zengqin School of Mathematical Sciences,Qufu Normal University,Qufu 273165,China
Abstract: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−20,1] positive solutions, and a sufficient condition, a necessary condition for the existence of C2n−10,1] 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.
Keywords:2nth-order differential equation  singular boundary value problem  fixed point theorem  positive solution  
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