Topological degree for a class of operators and applications

Abstract

The topological degree for a class of operators and it's use to solve a strongly singular nonlinear elliptic equation were discussed. N was used as an integer≥2. The topological degree due to it's homotopy property depended only on the values of f, a mapping from D ̄, on δ D and the boundary of D. The Leray-Schauder topological degree required conditions on f in the whole D̄. Skrypnik suggested that topological degree can be defined with conditions on f only onδ D.