A generalization of the Ekeland variational principle

TL;DR

This paper extends the Ekeland variational principle by incorporating the second Gâteaux variation, offering a broader theoretical framework within functional analysis and calculus of variations.

Contribution

It introduces a novel generalization of the Ekeland variational principle using second Gâteaux variation, expanding its applicability.

Findings

Established a new variational principle involving second Gâteaux variation

Utilized standard tools of functional analysis and calculus of variations

Provides a theoretical foundation for further research in optimization

Abstract

In this short communication, we present a generalization of the Ekeland variational principle. The main result is established through standard tools of functional analysis and calculus of variations. The novelty here is a result involving the second G\^ateaux variation of the functional in question.