Miscellaneous Applications of Certain Minimax Theorems II


In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.

This is a preview of subscription content, access via your institution.


  1. 1.

    Denkowski, S.M., Papageorgiou, N.S.: An Introduction to Nonlinear Analysis: Theory. Kluwer Academic Publishers (2003)

  2. 2.

    Denkowski, S.M., Papageorgiou, N.S.: An Introduction to Nonlinear Analysis: Applications. Kluwer Academic Publishers (2003)

  3. 3.

    Pucci, P., Serrin, J.: A mountain pass theorem. J. Differential Equations 60, 142–149 (1985)

    MathSciNet  Article  Google Scholar 

  4. 4.

    Ricceri, B.: Structure, approximation et dépendance continue des solutions de certaines équations non linéaires. C. R. Acad. Sci. Paris, Série I(305), 45–47 (1987)

    MathSciNet  MATH  Google Scholar 

  5. 5.

    Ricceri, B.: Some topological mini-max theorems via an alternative principle for multifunctions. Arch. Math. (Basel) 60, 367–377 (1993)

    MathSciNet  Article  Google Scholar 

  6. 6.

    Ricceri, B.: On a topological minimax theorem and its applications. In: Ricceri, B., Simons, S. (eds.) Minimax Theory and Applications, pp 191–216. Kluwer Academic Publishers (1998)

  7. 7.

    Ricceri, B.: A further improvement of a minimax theorem of Borenshtein and Shul’man. J. Nonlinear Convex Anal. 2, 279–283 (2001)

    MathSciNet  MATH  Google Scholar 

  8. 8.

    Ricceri, B.: Minimax theorems for limits of parametrized functions having at most one local minimum lying in a certain set. Topol. Appl. 153, 3308–3312 (2006)

    MathSciNet  Article  Google Scholar 

  9. 9.

    Ricceri, B.: Recent advances in minimax theory and applications. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds.) Pareto Optimality, Game Theory and Equilibria, pp 23–52. Springer (2008)

  10. 10.

    Ricceri, B.: Nonlinear eigenvalue problems. In: Gao, D.Y., Motreanu, D. (eds.) Handbook of Nonconvex Analysis and Applications, pp 543–595. International Press (2010)

  11. 11.

    Ricceri, B.: A strict minimax inequality criterion and some of its consequences. Positivity 16, 455–470 (2012)

    MathSciNet  Article  Google Scholar 

  12. 12.

    Ricceri, B.: Energy functionals of Kirchhoff-type problems having multiple global minima. Nonlinear Anal. 115, 130–136 (2015)

    MathSciNet  Article  Google Scholar 

  13. 13.

    Ricceri, B.: A minimax theorem in infinite-dimensional topological vector spaces. Linear Nonlinear Anal. 2, 47–52 (2016)

    MathSciNet  MATH  Google Scholar 

  14. 14.

    Ricceri, B.: Miscellaneous applications of certain minimax theorems I. Proc. Dynam. Systems Appl. 7, 198–202 (2016)

    MathSciNet  MATH  Google Scholar 

  15. 15.

    Ricceri, B.: On a minimax theorem: an improvement, a new proof and an overview of its applications. Minimax Theory Appl. 2, 99–152 (2017)

    MathSciNet  MATH  Google Scholar 

  16. 16.

    Rockafellar, R.T.: Integral Functionals, Normal Integrands and Measurable Selections. Lecture Notes in Math, vol. 543, pp 157–207. Springer, Berlin (1976)

    Google Scholar 

  17. 17.

    Tuy, H.: A new topological minimax theorem with application. J. Global Optim. 50, 371–378 (2011)

    MathSciNet  Article  Google Scholar 

Download references


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”.

Author information



Corresponding author

Correspondence to Biagio Ricceri.

Additional information

Dedicated to Professor Hoang Tuy with my greatest esteem

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ricceri, B. Miscellaneous Applications of Certain Minimax Theorems II. Acta Math Vietnam 45, 515–524 (2020). https://doi.org/10.1007/s40306-020-00369-z

Download citation


  • Minimax theorem
  • Connectedness
  • Global minimum
  • Multiplicity
  • Integral functional
  • Neumann problem

Mathematics Subject Classification (2010)

  • 49J35
  • 49K35
  • 49J45
  • 49K27
  • 35J92
  • 90C47