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The mountain pass theorem is an existence theorem from the calculus of variations, originally due to Antonio Ambrosetti and Paul Rabinowitz. Given certain conditions on a function, the theorem demonstrates the existence of a saddle point. The theorem is unusual in that there are many other theorems regarding the existence of extrema, but few regarding saddle points.

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  • Théorème du col (fr)
  • Teorema del passo montano (it)
  • Mountain pass theorem (en)
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  • Le théorème du col est un théorème d'existence du calcul des variations. Il établit l'existence d'un point col pour une fonction moyennant certaines conditions. L'originalité de ce théorème vient de ce qu'il existe beaucoup de théorèmes concernant l'existence d'extrema, mais peu sur les points col. (fr)
  • The mountain pass theorem is an existence theorem from the calculus of variations, originally due to Antonio Ambrosetti and Paul Rabinowitz. Given certain conditions on a function, the theorem demonstrates the existence of a saddle point. The theorem is unusual in that there are many other theorems regarding the existence of extrema, but few regarding saddle points. (en)
  • Il teorema del passo montano è un importante risultato in calcolo delle variazioni che dimostra, sotto certe ipotesi, l'esistenza di punti di sella per i funzionali. Tale teorema è spesso usato per dimostrare l'esistenza di soluzioni di equazioni differenziali o per dimostrare la non unicità di tali soluzioni. (it)
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  • Le théorème du col est un théorème d'existence du calcul des variations. Il établit l'existence d'un point col pour une fonction moyennant certaines conditions. L'originalité de ce théorème vient de ce qu'il existe beaucoup de théorèmes concernant l'existence d'extrema, mais peu sur les points col. (fr)
  • The mountain pass theorem is an existence theorem from the calculus of variations, originally due to Antonio Ambrosetti and Paul Rabinowitz. Given certain conditions on a function, the theorem demonstrates the existence of a saddle point. The theorem is unusual in that there are many other theorems regarding the existence of extrema, but few regarding saddle points. (en)
  • Il teorema del passo montano è un importante risultato in calcolo delle variazioni che dimostra, sotto certe ipotesi, l'esistenza di punti di sella per i funzionali. Tale teorema è spesso usato per dimostrare l'esistenza di soluzioni di equazioni differenziali o per dimostrare la non unicità di tali soluzioni. (it)
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