The index of an isolated critical point for a class of non-differentiable elliptic operators in reflexive Banach spaces

This paper is motivated by the problem of computing the index of an isolated critical point for a certain class of nonlinear elliptic operators. Such a class includes operators A which are defined by and are associated with boundary value problems of the type where , is open, bounded and has a C2-boundary ∂Ω. As an application of our new abstract theory, we obtain an index formula for such an operator A acting from the Sobolev space into its dual space for 1