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A further improvement of a minimax theorem of Borenshtein and Shulman
TLDR
This paper improved a recent improvement of a minimax theorem of Borenshtein and Shulamans, replacing a global compactness assumption by a local one. But they did not improve the local compactness of the theorem.Abstract:
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 oneread more
Citations
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Minimax theorems for limits of parametrized functions having at most one local minimum lying in a certain set
TL;DR: In this paper, the authors establish some minimax theorems, of purely topological nature, that, through the variational methods, can be usefully applied to nonlinear differential equations.
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A general multiplicity theorem for certain nonlinear equations in Hilbert spaces
TL;DR: In this article, the authors prove the following general result: for a real Hilbert space, X → R a continuously Gateaux differentiable, nonconstant functional, with compact derivative, such that for each r ∈ inf X J,sup X J[ for which the set J -1 ([r+∞]) is not convex and for each convex set S C X dense in X, there exist x 0 ∈ S ∩ J-1 (] - ∞, r[) and A > 0 such that the equation x= λ
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A new topological minimax theorem with application
TL;DR: A new topological minimax theorem is established for functions on C, where C is a topological space, and its proof is surprisingly simple.
Journal ArticleDOI
An extension of a multiplicity theorem by Ricceri with an application to a class of quasilinear equations
TL;DR: In this article, the multiplicity result by Ricceri, stated for equations in Hilbert spaces, is extended to a wider class of Banach spaces and applied to nonlinear boundary value problems involving the p-Laplacian.
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Miscellaneous applications of certain minimax theorems. I
TL;DR: In this article, the multiplicity of global minima for the integral functional of the Calculus of Variations is studied, and new applications of general minimax theorems are presented.
References
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Journal ArticleDOI
On a three critical points theorem
TL;DR: In this article, using a recent result by J. Saint Raymond, the authors improved the three critical points theorem established in [5] and [6] and showed that it can be improved further.
Book ChapterDOI
Minimax Theorems and Their Proofs
TL;DR: A minimax theorem is a theorem which asserts that, under certain conditions, a nonempty set is a minimax set as mentioned in this paper, i.e., a set whose members are nonempty sets.
Journal ArticleDOI
On the three critical points theorem
TL;DR: In this article, the Lusternik-Schnirel-man type is used to prove the three critical points theorem (TCPT) in the context of Banach spaces.
Journal ArticleDOI
A Minimax Theorem
TL;DR: A new, general criterion is given for ensuring that a closed saddle function has a nonempty compact set of saddlepoints and it is shown also that every minimaximizing sequence clusters around some saddlepoint.
BookDOI
Minimax theory and applications
Biagio Ricceri,Stephen Simons +1 more
TL;DR: Cheng et al. as mentioned in this paper proposed a two-function Minimax Theorem based on Horvath's minimax theorem and showed that it can be expressed as a topological investigation of the finite intersection property.