Acta mathematica scientia, Series B >
NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH#br# STRUM-LIOUVILLE BOUNDARY CONDITIONS
Received date: 2008-12-05
Revised date: 2010-03-23
Online published: 2011-07-20
Supported by
Research supported by the National Natural Science Foundation of China (10871116), the Natural Science Foundation of Shandong Province of China (ZR2010AM005) and the Doctoral Program Foundation of Education Ministry of China (200804460001).
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.
ZHAO Zeng-Qin . NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH#br# STRUM-LIOUVILLE BOUNDARY CONDITIONS[J]. Acta mathematica scientia, Series B, 2011 , 31(4) : 1569 -1582 . DOI: 10.1016/S0252-9602(11)60343-3
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