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On the variational principle

Ekeland, Ivar (1974), On the variational principle, Journal of Mathematical Analysis and Applications, 47, 2, p. 324-353. http://dx.doi.org/10.1016/0022-247X(74)90025-0

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OnTheVariationalPrinciple.pdf (1.096Mb)
Type
Article accepté pour publication ou publié
Date
1974
Journal name
Journal of Mathematical Analysis and Applications
Volume
47
Number
2
Publisher
Elsevier
Pages
324-353
Publication identifier
http://dx.doi.org/10.1016/0022-247X(74)90025-0
Metadata
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Author(s)
Ekeland, Ivar
Abstract (EN)
The variational principle states that if a differentiable functional F attains its minimum at some point View the MathML source, then View the MathML source; it has proved a valuable tool for studying partial differential equations. This paper shows that if a differentiable function F has a finite lower bound (although it need not attain it), then, for every ϵ > 0, there exists some point uϵ, where View the MathML source, i.e., its derivative can be made arbitrarily small. Applications are given to Plateau's problem, to partial differential equations, to nonlinear eigenvalues, to geodesics on infinite-dimensional manifolds, and to control theory.
Subjects / Keywords
variational principle

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