One result of Cauchy-Lagrange type (Q2785692)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: One result of Cauchy-Lagrange type |
scientific article; zbMATH DE number 981833
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | One result of Cauchy-Lagrange type |
scientific article; zbMATH DE number 981833 |
Statements
24 April 1997
0 references
Cauchy-Lagrange type theorem
0 references
existence of critical points for functionals
0 references
One result of Cauchy-Lagrange type (English)
0 references
Let \(C^1(E,\mathbb{R})\) be the set of continuously Frèchet differentiable functionals on a real Banach space \(E\). Then there holds the Mountain Pass Theorem [\textit{A. Ambrosetti} and \textit{P. H. Rabinowitz}, J. Funct. Anal. 14, 349-381 (1973; Zbl 0273.49063)]. Using this theorem, the author proves one general result of Cauchy-Lagrange type that allows to establish the existence of critical points for \(C^1(E,\mathbb{R})\) functionals. An application to nonlinear elliptic equations with Dirichlet boundary conditions is given.
0 references
