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

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

Show me the PDF file (255 KB), TEX file, and other files for this article.

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

Return to the EJDE web page