Advances in Difference Equations 
Volume 2004 (2004), Issue 2, Pages 93-109
doi:10.1155/S1687183904308071

On the existence and uniqueness of solutions to boundary value problems on time scales

Johnny Henderson,1 Allan Peterson,2 and Christopher C. Tisdell3

 1Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA
2Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0323, USA
3School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
Received 13 August 2003; Revised 11 February 2004

Abstract

This work formulates existence, uniqueness, and uniqueness-implies-existence theorems for solutions to two-point vector boundary value problems on time scales. The methods used include maximum principles, a priori bounds on solutions, and the nonlinear alternative of Leray-Schauder.