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 Stehlík1,2 and Christopher C. Tisdell2

 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

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.