Equivalence theorems and coincidence degree for multivalued mapping (Q1262523)

The main purpose of the paper is to develop a coincidence degree useful in the study of certain equations involving multivalued mappings. More precisely, if X and Y are normed spaces, L: D(L)\(\subset X\to Y\) is a linear operator and N: D(N)\(\subset X\to CK(Y)\), the author considers the inclusion L(x)\(\in N(x)\) \((CK(Y)=the\) family of compact convex subsets of Y). In this paper it is assumed that L is a linear Fredholm operator with index not necessarily zero. The class of multivalued mappings considered by the author is larger than the one used in the previous papers on this subject. The coincidence degree obtained is applied to a multivalued boundary value problem for an elliptic partial differential equation.