Towards a Morse theory on Banach spaces via ultrafunctions

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 “ultrafunctions” which solves some of the technical questions involved.

Keywords

• Non Archimedean Mathematics
• Non Standard Analysis
• Ultrafunctions
• Generalized solutions
• Critical point
• Morse index
• Morse theory