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Discrete Dirichlet boundary value problems with upper semicontinuous right-hand sides |
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| Authors: | Michal Fe?kan Hana Mach? |
| Institution: | 1. Department of Mathematical Analysis, Comenius University, Bratislava, Slovakia.;2. Mathematical Institute of Slovak Academy of Sciences, Bratislava, Slovakia.michal.feckan@fmph.uniba.sk;4. Faculty of Science, Department of Mathematical Analysis and Applications of Mathematics, Palacky University, Olomouc, Czech Republic. |
| Abstract: | This paper deals with the relationship between solutions of Dirichlet boundary value problems (BVPs) for second order systems of differential inclusions with upper semicontinuous right-hand sides and associated numerical discrete Dirichlet BVPs of second order difference inclusions. First, the existence and estimate of solutions to the discrete BVP is discussed uniformly with respect to the discrete step size. Then convergence of solutions of the numerical discrete BVP and the corresponding semicontinous BVP is studied. Related results are also mentioned which motivated our study of this problem. |
| Keywords: | Discrete multivalued Dirichlet problems upper semicontinuous problems existence results convergence of solutions |