International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 465867, 7 pages
http://dx.doi.org/10.1155/2012/465867
Research Article

Solution Matching for a Second Order Boundary Value Problem on Time Scales

Aprillya Lanz1 and Ana Tameru2

1Department of Mathematics and Computer Science, Virginia Military Institute, Lexington, VA 24450, USA
2Department of Mathematics and Computer Science, Alabama State University, 915 S. Jackson Street, Montgomery, AL 36101, USA

Received 7 June 2012; Revised 9 August 2012; Accepted 9 August 2012

Academic Editor: Palle E. Jorgensen

Copyright © 2012 Aprillya Lanz and Ana Tameru. 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

Let 𝕋 be a time scale such that 𝑎 < 𝑏 ; 𝑎 , 𝑏 ∈ 𝕋 . We will show the existence and uniqueness of solutions for the second-order boundary value problem 𝑦 Δ Δ ( 𝑡 ) = 𝑓 ( 𝑡 , 𝑦 ( 𝑡 ) , 𝑦 Δ ( 𝑡 ) ) , 𝑡 ∈ [ 𝑎 , 𝑏 ] 𝕋 , 𝑦 ( 𝑎 ) = 𝐴 , 𝑦 ( 𝑏 ) = 𝐵 , by matching a solution of the first equation satisfying boundary conditions on [ 𝑎 , 𝑐 ] 𝕋 with a solution of the first equation satisfying boundary conditions on [ 𝑐 , 𝑏 ] 𝕋 , where 𝑐 ∈ ( 𝑎 , 𝑏 ) 𝕋 .