Morse theory methods for a class of quasi-linear elliptic systems of higher order

TL;DR

This paper extends Morse theory to non-smooth functionals in Hilbert spaces, providing new splitting and perturbation results applicable to complex quasi-linear elliptic systems of higher order.

Contribution

It introduces a generalized splitting theorem and a weaker perturbation result for non-twice differentiable functionals, broadening Morse theory's applicability.

Findings

Developed local Morse theory for non-smooth functionals

Generalized Gromoll-Meyer's splitting theorem

Established a weaker Marino-Prodi perturbation result

Abstract

We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type result. They are applicable to a wide range of multiple integrals with quasi-linear elliptic Euler equations and systems of higher order.