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.Mathematics subject classification: 58E05, 26E30, 26E35, 35D99, 35A15.