Comparison and Contrast of the Classical (Ambrosetti and Rabinowitz) and Topological (Katriel) Approaches of the Mountain Pass Theorem

Abstract:

In this article we present the outlines of the proofs of the classical Mountain Pass Theorem by Ambrosetti and Rabinowitz and the topological Mountain Pass Theorem by Katriel. We study the particular applications of these theorems: existence of solutions for partial differential equations and homeomorphisms theorems, respectively. We prove that there exists a theorem in critical point theory in finite dimension that can be seen as a common application of both results. We made an analysis of the theoretical characteristics of the structure of the proofs of each theorem and finally we show if there is a logical relation between them.

Año de publicación:

2020

Keywords:

• General Topology
• Mountain Pass
• non-linear analysis
• partial differential equations

Fuente:

scopus