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Abstract and Applied Analysis
Volume 2014, Article ID 165429, 28 pages
http://dx.doi.org/10.1155/2014/165429
Research Article

Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications

School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

Received 6 February 2014; Accepted 6 April 2014; Published 11 May 2014

Academic Editor: Dragoş-Pătru Covei

Copyright © 2014 Jiang Zhu and Dongmei Liu. 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

Some delta-nabla type maximum principles for second-order dynamic equations on time scales are proved. By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.