Topological Degrees on Unbounded Domains

Let D be an open subset of RN and f : D → RN a continuous function. The classical topological degree for f demands that D be bounded. The boundedness of domains is also assumed for the topological degrees for compact displacements of the identity and for operators of monotone type in Banach spaces. In this work, we follow the methodology introduced by Nagumo for constructing topological degrees for functions on unbounded domains in finite dimensions and define the degrees for LeraySchauder operators and (S+)-operators on unbounded domains in infinite dimensions. Mathematics Subject Classification: Primary 47H14; Secondary 47H05, 47H11.