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Hartman-type conditions for multivalued Dirichlet problem in abstract spaces

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  • The classical Hartman's Theorem in [18] 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-Carathéodory 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.
    Mathematics Subject Classification: Primary: 34A60; Secondary: 34B15, 47H04.

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