Advances in Difference Equations
Volume 2009 (2009), Article ID 623932, 21 pages
doi:10.1155/2009/623932
Research Article

Positive Solution to a Singular p-Laplacian BVP with Sign-Changing Nonlinearity Involving Derivative on Time Scales

You-Hui Su,1 Subei Li,1 and Can-Yun Huang2

1School of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221008, China
2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China

Received 3 January 2009; Revised 4 March 2009; Accepted 24 March 2009

Academic Editor: Alberto Cabada

Copyright © 2009 You-Hui Su et al. 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.

Abstract

Let T be a time scale such that 0,T∈T. By using a monotone iterative method, we present some existence criteria for positive solution of a multiple point general Dirichlet-Robin BVP on time scales with the singular sign-changing nonlinearity. These results are even new for the corresponding differential (T=ℝ) and difference equation (T=ℤ) as well as in general time scales setting. As an application, an example is given to illustrate the results. The interesting point here is that the sign-changing nonlinear term is involved with the first-order derivative explicitly, and the singularity may occur at u=0, t=0, and t=T.