Advances in Difference Equations
Volume 2011 (2011), Article ID 378686, 9 pages
doi:10.1155/2011/378686
Research Article

On the Existence of Solutions for Dynamic Boundary Value Problems under Barrier Strips Condition

Hua Luo1 and Yulian An2

1School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China
2Department of Mathematics, Shanghai Institute of Technology, Shanghai 200235, China

Received 24 November 2010; Accepted 20 January 2011

Academic Editor: Jin Liang

Copyright © 2011 Hua Luo and Yulian An. 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

By defining a new terminology, scatter degree, as the supremum of graininess functional value, this paper studies the existence of solutions for a nonlinear two-point dynamic boundary value problem on time scales. We do not need any growth restrictions on nonlinear term of dynamic equation besides a barrier strips condition. The main tool in this paper is the induction principle on time scales.