Electron. J. Diff. Eqns., Vol. 2007(2007), No. 19, pp. 1-12.

Third-order nonlocal problems with sign-changing nonlinearity on time scales

Douglas R. Anderson, Christopher C. Tisdell

We are concerned with the existence and form of positive solutions to a nonlinear third-order three-point nonlocal boundary-value problem on general time scales. Using Green's functions, we prove the existence of at least one positive solution using the Guo-Krasnoselskii fixed point theorem. Due to the fact that the nonlinearity is allowed to change sign in our formulation, and the novelty of the boundary conditions, these results are new for discrete, continuous, quantum and arbitrary time scales.

Submitted October 31, 2006. Published January 27, 2007.
Math Subject Classifications: 4B18, 34B27, 34B10, 39A10.
Key Words: Boundary value problem; time scale; three-point; Green's function.

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Douglas R. Anderson
Department of Mathematics and Computer Science
Concordia College
Moorhead, MN 56562 USA
email: andersod@cord.edu
Christopher C. Tisdell
School of Mathematics
The University of New South Wales
UNSW Sydney 2052, Australia
email: cct@maths.unsw.edu.au

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