“…This result (and different variations of it) is widely used to prove existence and uniqueness theorems for operator equations, partial differential equations and variational inequalities (see [19]). Surprisingly, in the finite dimensional case this result boils down just to the continuity and expansivity of A + I, beeing a particular case (it is not trivial to show) of a classical homeomorphism theorem of Browder [4, Theorem 4.10] (connected to this subject see also [1]- [3], [6], [13]- [15].) We shall generalize this result for a complete connected Riemannian manifold M .…”