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 Henderson1
, Allan Peterson2
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
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.