Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 79653, 17 pages
Existence and multiplicity of solutions for some three-point nonlinear boundary value problems
1Department of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu 221116, China
2Department of Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland
Received 30 September 2004; Accepted 20 October 2004
Copyright © 2006 Xu Xian and Donal O'Regan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the existence and multiplicity of solutions for the
three-point nonlinear boundary value problem , ; , where , , and are assumed to be positive and have some singularities, and is a positive parameter. Under certain conditions, we prove that there
exists such that the three-point nonlinear
boundary value problem has at least two positive solutions for , at least one solution for , and no solution for .