# Miscellaneous Applications of Certain Minimax Theorems II

@article{Ricceri2020MiscellaneousAO, title={Miscellaneous Applications of Certain Minimax Theorems II}, author={Biagio Ricceri}, journal={Acta Mathematica Vietnamica}, year={2020}, volume={45}, pages={515-524} }

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.

## 6 Citations

On a minimax theorem: an improvement, a new proof and an overview of its applications

- Mathematics
- 2016

Theorem 1 of [14], a minimax result for functions $f:X\times Y\to {\bf R}$, where $Y$ is a real interval, was partially extended to the case where $Y$ is a convex set in a Hausdorff topological…

A more complete version of a minimax theorem

- Mathematics
- 2021

In this paper, we present a more complete version of the minimax theorem established in [7]. As a consequence, we get, for instance, the following result: Let X be a compact, not singleton subset of…

A Class of Equations with Three Solutions

- Mathematics, Physics
- 2020

Here is one of the results obtained in this paper: Let $\Omega\subset {\bf R}^n$ be a smooth bounded domain, let $q>1$, with $q \lambda_1$ and for every convex set $S\subseteq L^{\infty}(\Omega)$…

A class of functionals possessing multiple global minima

- Physics, Mathematics
- 2020

We get a new multiplicity result for gradient systems. Here is a very particular corollary: Let $\Omega\subset {\bf R}^n$ ($n\geq 2$) be a smooth bounded domain and let $\Phi:{\bf R}^2\to {\bf R}$ be…

An alternative theorem for gradient systems.

- Mathematics, Physics
- 2020

Here is one of the result obtained in this paper: Let $\Omega\subset {\bf R}^2$ be a smooth bounded domain and let $F, G : {\bf R}\to {\bf R}$ be two $C^1$ functions satisfying the following…

## References

SHOWING 1-10 OF 30 REFERENCES

Recent Advances in Minimax Theory and Applications

- Mathematics
- 2008

In this chapter, we give an overview of various applications of a recent minimax theorem. Among them, there are some multiplicity theorems for nonlinear equations as well as a general well-posedness…

A Further Improvement of a Minimax Theorem of Borenshtein and Shul'Man

- Mathematics
- 2001

I do improve a recent improvement (due to Saint Raymond) of a minimax theorem of Borenshtein and Shul'man, replacing a global compactness assumption by a local one.

A new topological minimax theorem with application

- Mathematics, Computer ScienceJ. Glob. Optim.
- 2011

A new topological minimax theorem is established for functions on C, where C is a topological space, and its proof is surprisingly simple.

The Mountain-Pass Theorem

- Mathematics
- 2007

Roughly speaking, the basic idea behind the so-called minimax method is the following: Find a critical value of a functional ϕ ∈ C1 (X, ℝ) as a minimax (or maximin) value c ∈ ℝ of ϕ over a suitable…

Minimax theorems for limits of parametrized functions having at most one local minimum lying in a certain set

- Mathematics
- 2006

In this paper, we establish some minimax theorems, of purely topological nature, that, through the variational methods, can be usefully applied to nonlinear differential equations. Here is a…

A strict minimax inequality criterion and some of its consequences

- Physics, Mathematics
- 2012

In this paper, we point out a very flexible scheme within which a strict minimax inequality occurs. We then show the fruitfulness of this approach presenting a series of various consequences. Here is…

On a minimax theorem: an improvement, a new proof and an overview of its applications

- Mathematics
- 2016

Theorem 1 of [14], a minimax result for functions $f:X\times Y\to {\bf R}$, where $Y$ is a real interval, was partially extended to the case where $Y$ is a convex set in a Hausdorff topological…

Some topological mini-max theorems via an alternative principle for multifunctions

- Mathematics
- 1993

does hold. The relevant literature is by now really impressive. For a first approach to it, we refer the reader to the references quoted in [4], [5], [7], [9]. However, as well stressed by the lucid…

Integral functionals, normal integrands and measurable selections

- Mathematics
- 1976

Abstract : A fundamental notion in many areas of mathematics, including optimal control, stochastic programming, and the study of partial differential equations, is that of an integral functional. By…

Energy functionals of Kirchhoff-type problems having multiple global minima

- Mathematics
- 2014

In this paper, using the theory developed in [8], we obtain some results of a totally new type about a class of non-local problems. Here is a sample:
Let $\Omega\subset {\bf R}^n$ be a smooth…