Open Access Research

Dirichlet problem in Banach spaces: the bound sets approach

Jan Andres1*, Luisa Malaguti2 and Martina Pavlačková1

Author Affiliations

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

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Boundary Value Problems 2013, 2013:25  doi:10.1186/1687-2770-2013-25

Published: 11 February 2013

Abstract

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.

Keywords:
Dirichlet problem; bounding functions; solutions in a given set; condensing multivalued operators