Abstract
The paper is concerned with certain aspects of a theory of critical points of a scalar (i.e., a real valued funct ion) i(5) defined in a Hilbert space H, especially with the relation of the cr i t ica l points to the gradient field of i(~). Moreover, applications to the theory of non-linear integral equations are made. Le t V be a bounded open convex set of H, and S its boundary. We suppose t ha t i(~) is defined in an open region V' conta ining V + S in its interior. I f i(5) is wri t ten in the form
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