Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 107, pp. 1-15.

Title: Existence of solutions to a third-order 
       multi-point problem on time scales

Authors: Douglas R. Anderson (Concordia College, Moorhead, MN, USA)
         Joan Hoffacker (Clemson Univ., Clemson, SC USA)

Abstract: 
 We are concerned with the existence and form of solutions to nonlinear
 third-order three-point and multi-point boundary-value problems on
 general time scales. Using the corresponding Green function,
 we prove the existence of at least one positive solution using
 the Guo-Krasnosel'skii fixed point theorem. Moreover, a third-order
 multi-point eigenvalue problem is formulated, and eigenvalue intervals
 for the existence of a positive solution are found.

Submitted July 8, 2007. Published August 07, 2007.
Math Subject Classifications: 34B18, 34B27, 34B10, 39A10.
Key Words: Boundary value problem; time scale; third order;
           Green function.