On the applications of a minimax theorem

Abstract

In this paper, we give an overview of some recent applications of a minimax theorem. These applications deal with: uniquely remotal sets in normed spaces; multiple global minima for the integral functional of the Calculus of Variations; multiple periodic solutions for Lagrangian systems of relativistic oscillators; variational inequalities in balls of Hilbert spaces.

Keywords:

• Minimax theorem
• uniquely remotal set
• integral functional
• Lagrangian system of relativistic oscillators
• variational inequality

2010 Mathematics Subject Classifications:

• 34A34
• 34C25
• 47J20
• 49J35
• 49J45
• 49J40
• 49K27
• 49K35
• 90C47

Acknowledgments

The author wishes to thank the referees for their comments. The author has been supported by the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by the Università degli Studi di Catania, ‘Piano della Ricerca 2016/2018 Linea di intervento 2’.

Disclosure statement

No potential conflict of interest was reported by the author(s).