Electron. J. Diff. Eqns., Vol. 2007(2007), No. 149, pp. 1-12.

Two classical periodic problems on time scales

Pablo Amster, Christopher C. Tisdell

We consider the generalization of two classical periodic problems to the context of time scales. On the one hand, we generalize a celebrated result by Castro for the forced pendulum equation. On the other hand, we extend a well-known result by Nirenberg to a resonant system of equations on time scales. Furthermore, the results are new even for classical difference equations.

Submitted April 3, 2007. Published November 9, 2007.
Math Subject Classifications: 39A12, 39A99.
Key Words: Time scale; boundary value problem; forced pendulum equation; Landesman-Lazer conditions; existence of solutions.

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Pablo Amster
Departamento de Matemática
Universidad de Buenos Aires
Ciudad Universitaria, Pabellóon I
(1428) Buenos Aires, Argentina
email: pamster@dm.uba.ar
Christopher C. Tisdell
School of Mathematics
The University of New South Wales
Sydney, NSW, 2052, Australia
email: cct@maths.unsw.edu.au

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