The classical Hartman’s Theorem in for the solvability of the vector Dirichlet problem will be generalized and extended in several directions. We will consider its multivalued versions for Marchaud and upper-Carath´eodory right-hand sides with only certain amount of compactness in Banach spaces. Advanced topological methods are combined with a bound sets technique. Besides the existence, the localization of solutions can be obtained in this way.
Hartman-type conditions for multivalued Dirichlet problem in abstract spaces / Andres, Jan; Malaguti, Luisa; Pavlačková, Martina. - STAMPA. - Issue special(2015), pp. 38-55. (Intervento presentato al convegno 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications tenutosi a Madrid (Spagna) nel 7-11 luglio, 2014) [10.3934/proc.2015.0038].
Hartman-type conditions for multivalued Dirichlet problem in abstract spaces
MALAGUTI, Luisa;
2015-01-01
Abstract
The classical Hartman’s Theorem in for the solvability of the vector Dirichlet problem will be generalized and extended in several directions. We will consider its multivalued versions for Marchaud and upper-Carath´eodory right-hand sides with only certain amount of compactness in Banach spaces. Advanced topological methods are combined with a bound sets technique. Besides the existence, the localization of solutions can be obtained in this way.
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