Boundary Value Problems
Volume 2005 (2005), Issue 2, Pages 153-163
doi:10.1155/BVP.2005.153
On boundary value problems for second-order discrete inclusions
Petr Stehlík1
and Christopher C. Tisdell2
1Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 22, Plze {n} 306 14, Czech Republic
2School of Mathematics, The University of New South Wales, Sydney NSW 2052, Australia
Abstract
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.