Electron. J. Diff. Eqns., Vol. 2007(2007), No. 107, pp. 1-15.

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

Douglas R. Anderson, Joan Hoffacker

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 7, 2007.
Math Subject Classifications: 34B18, 34B27, 34B10, 39A10.
Key Words: Boundary value problem; time scale; third order; Green function.

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Douglas R. Anderson
Department of Mathematics and Computer Science
Concordia College
Moorhead, MN 56562 USA
email: andersod@cord.edu
  Joan Hoffacker
Department of Mathematical Sciences
Clemson University
Clemson, SC 29634 USA
email: johoff@clemson.edu

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