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 |
本文献已被 CNKI 维普 ScienceDirect 等数据库收录! |