Boundary Value Problems
Volume 2005 (2005), Issue 2, Pages 153-163
On boundary value problems for second-order discrete inclusions
1Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 22, Plzeň 306 14, Czech Republic
2School of Mathematics, The University of New South Wales, Sydney NSW 2052, Australia
Received 8 October 2004
Copyright © 2005 Petr Stehlík and Christopher C. Tisdell. 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 prove some existence theorems regarding solutions to boundary
value problems for systems of second-order discrete inclusions.
For a certain class of right-hand sides, we present some lemmas
showing that all solutions to discrete second-order inclusions
satisfy an a priori bound. Then we apply these a
priori bounds, in conjunction with an appropriate fixed point
theorem for inclusions, to obtain the existence of solutions. The
theory is highlighted with several examples.