International Journal of Difference Equations
  • Year: 2007
  • Volume: 2
  • Issue: 1

Variational Methods for Two Resonant Problems on Time Scales*

  • Author:
  • P. Amster1, P. De Nápoli1, C. C. Tisdell2
  • Total Page Count: 12
  • Page Number: 1 to 12

1Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina and Consejo Nacional de Investigaciones, Científicas y Técnicas (CONICET), Argentina. E-mail: pamster@dm.uba.ar, pdenapo@dm.uba.ar

2School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW, 2052, Australia. E-mail: cct@unsw.edu.au

*This research was supported under theAustralian Research Council's Discovery Projects (DP0450752) and Consejo Nacional de Investigaciones Científicas y Técnicas-Argentina (PIP 5477).

Abstract

Using variational methods we study the generalization of two classical second order periodic problems in the context of time scales. On the one hand, we study a forced pendulum-type equation. On the other hand, we obtain solutions for a bounded nonlinearity under Landesman–Lazer type conditions.

Keywords

Time scale, resonant boundary value problem, Sobolev spaces, variational methods.