Dirichlet problem in Banach spaces: the bound sets approach
1 Department of Mathematical Analysis, Faculty of Science, Palacký University, 17. listopadu 12, Olomouc, 771 46, Czech Republic
2 Department of Engineering Sciences and Methods, University of Modena and Reggio Emilia, Via G. Amendola, 2 - pad. Morselli, Reggio Emilia, I-42122, Italy
Boundary Value Problems 2013, 2013:25 doi:10.1186/1687-2770-2013-25Published: 11 February 2013
The existence and localization result is obtained for a multivalued Dirichlet problem in a Banach space. The upper-Carathéodory and Marchaud right-hand sides are treated separately because in the latter case, the transversality conditions derived by means of bounding functions can be strictly localized on the boundaries of bound sets.
MSC: 34A60, 34B15, 47H04.