Comparación y contraste de los enfoques clásico (Ambrosseti y Rabinowitz) y topológico (Katriel) del teorema de mountain pass (paso de montaña)

Abstract

The main objective of this work is to discover the motivations, relations —of theoretical and logic nature— and practical scope of two approaches of the mountain pass theorem: the classical and the topological one. For this, a review of the theoretical elements needed for the proof of the classical theorem is done; the actual proof is carried out in detail. Then, an application of the theorem, with original input, is recreated extensively. After that, the proof of the topological theorem is executed, for which, one more time, the theory to understand it completely is reviewed; once again, its applications are studied. Both proofs are adapted in order to carry out the exercise of comparison and contrast that is presented in the last part, in which the elements that aloud to see clearly the common and diversification points between both versions are showed. The emphasis is put in the relations between its affined applications, theoretical elements of the proofs and logic relations between the two theorems. Finally, conclusions are presented.