Green's function and positive solutions of a singular nth-order three-point boundary value problem on time scales
Dapeng Xie, Hefei Teachers College, Hefei, Anhui, P. R. China E. J. Qualitative Theory of Diff. Equ., No. 38. (2009), pp. 1-14.
Yang Liu, Hefei Teachers College, Hefei, Anhui, P. R. China
Chuanzhi Bai, Huaiyin Teachers College, Huaian, Jiangsu, P. R. China
| Communicated by P. Eloe. | Received on 2008-10-26 Appeared on 2009-06-15 |
Abstract: In this paper, we investigate the existence of positive solutions for a class of singular $n$th-order three-point boundary value problem. The associated Green's function for the boundary value problem is given at first, and some useful properties of the Green's function are obtained. The main tool is fixed-point index theory. The results obtained in this paper essentially improve and generalize some well-known results.
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