Existence of solutions to second-order BVPs on time scales

Abstract

We consider a boundary value problem (BVP) for systems of second-order dynamic equations on time scales. Using methods involving dynamic inequalities, we formulate conditions under which all solutions to a certain family of systems of dynamic equations satisfy certain a priori bounds. These results are then applied to guarantee the existence of solutions to BVPs for systems of dynamic equations on time scales.

Keywords:

• Boundary value problem
• System of equations
• Time scale
• Dynamic equation
• Existence of solutions
• AMS Subject Classifications: 39A10
• 39A99

Acknowledgments

This research was supported by NSF Grant 0072505 and The Australian Research Council's Discovery Projects (DP0450752), The Australian Academy of Science's “Scientific Visits Program” and The University of New South Wales.

Notes

Email: [email protected]

Email: [email protected]

Email: [email protected]

Additional information

Notes on contributors

Christopher C. Tisdell ¶

Email: [email protected] Email: [email protected]