SPECULATING ABOUT MOUNTAINS
Nadezhda K. Ribarska, Y. Tsachev, Mikhail Ivanov Krastanov · 1996
Abstract. 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. 0. Introduction. The classical mountain pass theorem of A. Ambrosetti and P.H.Rabinowitz (cf. [1]) has been extended in various directions, one of them being the relaxation of the smoothness assumption on the considered functional. These extensions require notions corresponding to the norm of the derivative (and in particular, to a critical point) in the C 1 case. A well known generalization is for locally Lipschitz