Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case. We apply these techniques to describe a strategy for addressing the Wilkinson problem of calculating the distance from a matrix to a closest matrix w...

this text carries out some ideas about exact and p− exact sequences of transformationsemigroups. some theorems like the short five lemma (lemma 1.3 and lemma 2.3) are valid here as inexact sequences of r − modules.

In this paper we show the existence and multiplicity of positive solutions using sub-supersolution method Mountain Pass Theorem in a general singular system which operator is not homogeneous neither linear.