A Scorza-Dragoni approach to Dirichlet problem with an upper-Carathéodory right-hand side

Abstract

In this paper, the existence and localization result will be proven for multivalued vector Dirichlet problem with an upper-Carathéodory right-hand side by using bound sets approach. Since Scorza-Dragoni type technique will be furthermore applied, the conditions for bounding functions can be required directly on the boundaries of bound sets and not at some vicinity of them.