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On the variational principle. (English) Zbl 0286.49015


MSC:

49K27 Optimality conditions for problems in abstract spaces
49M99 Numerical methods in optimal control
49R05 Variational methods for eigenvalues of operators
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
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References:

[1] Abraham; Robbin, Transversal Mappings and Flows (1967), Benjamin: Benjamin New York · Zbl 0171.44404
[2] Asplund, Frechet differentiability of convex functions, Acta Math., 121, 31-47 (1968) · Zbl 0162.17501
[3] Baranger, Existence de solutions pour des problèmes d’optimisation non convexes, C. R. Acad. Sci. Paris, 274, 307-309 (1972) · Zbl 0231.46039
[4] Bishop; Phelps, The support functional of a convex set, (Klee, Convexity. Convexity, Proc. Symp. Pure Math., Vol. 7 (1963), Amer. Math. Soc: Amer. Math. Soc Providence, RI), 27-35
[5] Bourbaki, Variétés différentielles et analytiques (1970), Hermann: Hermann New York
[6] Bronsted; Rockafellar, On the subdifferentiability of convex functions, (Proc. AMS, 16 (1965)), 605-611 · Zbl 0141.11801
[7] Browder, Normal solvability for non linear mappings into Banach spaces, Bull. AMS, 79, 328-350 (1973)
[8] Dowling, Finsler geometry on Sobolev manifolds, (Global Analysis. Global Analysis, Proc. Symp. Pure Math., Vol. 15 (1968), Amer. Math. Soc: Amer. Math. Soc Berkeley, CA) · Zbl 0217.20601
[9] Ebin, Espace des métriques riemanniennes et mouvement des fluides via les variétés d’applications, (Lecture Notes (1971-1972), Centre de Mathématiques de l’École Polytechnique) · Zbl 0242.58002
[10] Edelstein, Farthest points of set in uniformly convex Banach spaces, Israēl J. Math., 4, 171-176 (1966) · Zbl 0151.17601
[11] Edelstein, On nearest points of sets in uniformly convex Banach spaces, J. London Math. Soc., 43, 375-377 (1968) · Zbl 0183.40403
[12] Eels, Asetting for globalanalysis, Bull. Amer. Math. Soc., 751-807 (1966)
[13] Ekeland, Sur le contröle optimal de systèmes gouvernés par des équations elliptiques, J. Functional Analysis, 9, 1-62 (1972) · Zbl 0227.49001
[14] Ekeland; Temam, Analyse convexe et problèmes variationnels (1974), Dunod-Gauthier-Villars: Dunod-Gauthier-Villars Paris · Zbl 0281.49001
[15] Eliasson, Variation integrals in fiber bundles, (Global Analysis, Proc. Symp. Pure Math. AMS, 16 (1968)), Berkeley · Zbl 0205.51802
[16] Grossmann, Geodesics on Hilbert manifolds, (Ph.D. Thesis (1964), Univ. of Minnesota)
[17] Krasnoselski, Topological methods in the theory of nonlinear integral equations (1963), Pergamon Press: Pergamon Press New York
[18] Lang, Differential Manifolds (1970), Addison-Wesley: Addison-Wesley Reading, MA
[19] MacAlpin, Infinite Dimensional Manifolds and Morse Theory, (Ph.D. Thesis (1965), Columbia Univ)
[20] Palais, Foundations of Global Nonlinear Analysis (1968), Benjamin: Benjamin New York · Zbl 0164.11102
[21] Palais, Banach manifolds of fibre bundle sections, (Congrès Int. des Mathématiciens. Congrès Int. des Mathématiciens, Nice (1970)) · Zbl 0326.58008
[22] Palais, Morse theory on Hilbert manifolds, Topology, 2, 299-340 (1963) · Zbl 0122.10702
[23] Palais-Smale, Ageneralized Morse theory, Bull. Amer. Math. Soc., 70, 165-171 (1964) · Zbl 0119.09201
[24] de la Barrière, Pallu, Cours d’automatique théorique (1965), Dunod · Zbl 0133.39601
[25] Penot, Diverses Méthodes de Construction de Variétés d’Applications, (Thesis (1970), Univ. of Paris)
[26] Penot, Topologie faibles sur des variétés de Banach. Application aux géodésiques des variétés de Sobolev (1972), preprint · Zbl 0238.58005
[27] Smale, Morse theory and a non-linear generalization of the Dirichlet problem, Ann. Math., 80, 382-396 (1964) · Zbl 0131.32305
[28] Uhlenbeck, The calculus of variations and global analysis, (Ph.D. Thesis (1968), Brandeis Univ) · Zbl 0208.12802
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