Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 845107, 8 pages
http://dx.doi.org/10.1155/2011/845107
Research Article

First-Order Boundary Value Problem with Nonlinear Boundary Condition on Time Scales

Ya-Hong Zhao

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 16 March 2011; Accepted 2 June 2011

Academic Editor: Wei-Der Chang

Copyright © 2011 Ya-Hong Zhao. 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

This work is concerned with the following first-order dynamic equation on time scale 𝕋 ,   𝑥 Δ ( 𝑡 ) + 𝑝 ( 𝑡 ) 𝑥 ( 𝜎 ( 𝑡 ) ) = 𝑓 ( 𝑡 , 𝑥 ( 𝑡 ) ) , 𝑡 ∈ [ 0 , 𝑇 ] 𝕋 with the nonlinear boundary condition 𝑥 ( 0 ) = 𝑔 ( 𝑥 ( 𝜎 ( 𝑇 ) ) ) . By applying monotone iteration method, we not only obtain the existence of positive solutions, but also establish iterative schemes for approximating the solutions.