Scorza-Dragoni approach to Dirichlet problem in Banach spaces
Ján Andres, Luisa Malaguti, Martina Pavlačková · Boundary Value Problems · 2014
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.