On Struwe-Jeanjean-Toland monotonicity trick

TL;DR

This paper improves and extends Struwe's monotonicity trick, originally for smooth functionals, to continuous, non-smooth functionals on Banach spaces, broadening its applicability in critical point theory.

Contribution

It enhances the monotonicity trick for non-smooth functionals and extends its framework to Banach spaces, enabling new applications in variational analysis.

Findings

Extended the monotonicity trick to continuous functionals

Generalized the approach to Banach spaces

Broadened the scope of non-smooth critical point theory

Abstract

The abstract version of Struwe's monotonicity trick developed by Jeanjean and Jeanjean-Toland for functionals depending on a real parameter is improved, under suitable assumptions. Besides, all the machinery is extended to the case of continuous functionals on Banach spaces, in the framework of non-smooth critical point theory.