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Abstract and Applied Analysis
Volume 2009, Article ID 512402, 21 pages
Research Article

Existence of Positive Solutions to Singular 𝑝 -Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity

1College of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China
2School of Mathematics and Physics, XuZhou Institute of Technology, Xuzhou, Jiangsu 221008, China
3Department of Mathematics, Hexi University, Zhangye, Gansu 734000, China

Received 27 December 2008; Revised 21 February 2009; Accepted 25 February 2009

Academic Editor: Paul Eloe

Copyright © 2009 Qiying Wei 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.


By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an 𝑚 -point singular 𝑝 -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential ( 𝕋 = ) and difference equations ( 𝕋 = ), as well as in general time scales setting. As an application, an example is given to illustrate the results.