be a complete metric space and
be continuous. The authors define the notion of weak slope
, which corresponds to
are of class
. The definition is based on the existence of certain deformations of neighborhoods of
decreases. Using these local deformations the authors prove a version of the deformation lemma. If
satisfies the Palais-Smale condition abstract critical point theorems follow in a standard way. No use is made of Ekeland’s variational principle. Under additional assumptions the theory can be generalized to lower semi-continuous functions.