Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 371285, 13 pages
doi:10.1155/2010/371285
Research Article

Positive Solutions for System of First-Order Dynamic Equations

Da-Bin Wang,1 Jian-Ping Sun,1 and Xiao-Jun Li2

1Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
2School of Science, Hohai University, Nanjing, Jiangsu 210098, China

Received 23 September 2009; Accepted 12 April 2010

Academic Editor: Juan Jose Nieto

Copyright © 2010 Da-Bin Wang 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.

Abstract

We study the existence of positive solutions to the system of nonlinear first-order periodic boundary value problems on time scales xΔ(t)+P(t)x(σ(t))=F(t,x(σ(t))), t∈[0,T]T, x(0)=x(σ(T)), by using a well-known fixed point theorem in cones. Moreover, we characterize the eigenvalue intervals for xΔ(t)+P(t)x(σ(t))=λH(t)G(x(σ(t))), t∈[0,T]T, x(0)=x(σ(T)).