Academic Editor: J. Mawhin
Copyright © 2010 M. Frigon and H. Gilbert. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We establish the existence of solutions to systems of second-order
dynamic equations on time scales with the right member , a -Carathéodory
function. First, we consider the case where the nonlinearity does not depend
on the -derivative, (). We obtain existence results for Strum-Liouville and
for periodic boundary conditions. Finally, we consider more general systems
in which the nonlinearity depends on the -derivative and satisfies a linear
growth condition with respect to (). Our existence results rely on notions
of solution-tube that are introduced in this paper.