Towards a Morse theory on Banach spaces via ultrafunctions

TL;DR

This paper introduces ultrafunctions, a new type of generalized functions, to develop Morse theory on Banach spaces, addressing key technical challenges in nonlinear analysis.

Contribution

It proposes a novel approach using ultrafunctions to overcome technical obstacles in extending Morse theory to Banach spaces.

Findings

Ultrafunctions provide a new framework for Morse theory on Banach spaces.

The approach addresses specific technical problems in nonlinear analysis.

Potential applications in nonlinear analysis and related fields.

Abstract

Morse Theory on Banach spaces would be a useful tool in nonlinear analysis but its development is hindered by many technical problems. In this paper we present an approach based on a new notion of generalized functions called \textquotedblleft ultrafunctions\textquotedblright\ which solves some of the technical questions involved.