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Open Access Research

Scorza-Dragoni approach to Dirichlet problem in Banach spaces

Jan Andres1*, Luisa Malaguti2 and Martina Pavlačková1

Author Affiliations

1 Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, Olomouc, 771 46, Czech Republic

2 Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via G. Amendola, 2 - pad. Morselli, Reggio Emilia, 42122, Italy

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Boundary Value Problems 2014, 2014:23  doi:10.1186/1687-2770-2014-23

Published: 27 January 2014

Abstract

Hartman-type conditions are presented for the solvability of a multivalued Dirichlet problem in a Banach space by means of topological degree arguments, bounding functions, and a Scorza-Dragoni approximation technique. The required transversality conditions are strictly localized on the boundaries of given bound sets. The main existence and localization result is applied to a partial integro-differential equation involving possible discontinuities in state variables. Two illustrative examples are supplied. The comparison with classical single-valued results in this field is also made.

MSC: 34A60, 34B15, 47H04.

Keywords:
Dirichlet problem; Scorza-Dragoni-type technique; strictly localized bounding functions; solutions in a given set; condensing multivalued operators