Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Abstract
∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology,
Bulgaria.
∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Science
and Technology, Bulgaria.The definition of the weak slope of continuous functions introduced by
Degiovanni and Marzocchi (cf. [8]) and its interrelation with the notion “steepness”
of locally Lipschitz functions are discussed. A deformation lemma and a mountain
pass theorem for usco mappings are proved. The relation between these results
and the respective ones for lower semicontinuous functions (cf. [7]) is considered
