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

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

You-Hui Su1 , Subei Li1 and Can-Yun Huang3

1School of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221008, China
3Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China

Abstract

Let T be a time scale such that 0,TT. 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=) and difference equation (T=) 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.