Hindawi Publishing Corporation Boundary Value Problems Volume 2011, Article ID 867615, 17 pages doi: Research Article Multiple Positive Solutions for Second-Order p-Laplacian Dynamic Equations with Integral Boundary Conditions Yongkun Li and Tianwei Zhang Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China Correspondence should be addressed to Yongkun Li, yklie@ Received 13 July 2010; Revised 21 November 2010; Accepted 25 November 2010 Academic Editor: Gennaro Infante Copyright q 2011 Y. Li and T. Zhang. 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. | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 867615 17 pages doi 2011 867615 Research Article Multiple Positive Solutions for Second-Order p-Laplacian Dynamic Equations with Integral Boundary Conditions Yongkun Li and Tianwei Zhang Department of Mathematics Yunnan University Kunming Yunnan 650091 China Correspondence should be addressed to Yongkun Li yklie@ Received 13 July 2010 Revised 21 November 2010 Accepted 25 November 2010 Academic Editor Gennaro Infante Copyright 2011 Y. Li and T. Zhang. 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 are concerned with the following second-order p-Laplacian dynamic equations on time scales tfp xA t v Xf t x t xA t 0 t e 0 T t with integral boundary conditions xA 0 0 ax T - fx 0 J0 g s x s Vs. By using Legget-Williams fixed point theorem some criteria for the existence of at least three positive solutions are established. An example is presented to illustrate the main result. 1. Introduction Boundary value problems with p-Laplacian have received a lot of attention in recent years. They often occur in the study of the n-dimensional p-Laplacian equation non-Newtonian fluid theory and the turbulent flow of gas in porous medium 1-7 . Many works have been carried out to discuss the existence of solutions or positive solutions and multiple solutions for the local or nonlocal boundary value problems. On the other hand the study of dynamic equations on time scales goes back to its founder Stefan Hilger 8 and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on time scales can build bridges between continuous and discrete equations. Further the study of time scales has led to several important applications for example in the study of insect .
