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On the variational principle. (English) Zbl 0286.49015

49K27Optimal control problems in abstract spaces (optimality conditions)
49M99Numerical methods in calculus of variations
49R05Variational methods for eigenvalues of operators
49Q15Geometric measure and integration theory, integral and normal currents (optimization)
58B20Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
Full Text: DOI
[1] Abraham; Robbin: Transversal mappings and flows. (1967) · Zbl 0171.44404
[2] Asplund: Fréchet differentiability of convex functions. Acta math. 121, 31-47 (1968)
[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. Proc. symp. Pure math. 7, 27-35 (1963) · Zbl 0149.08601
[5] Bourbaki: Variétés différentielles et analytiques. (1970)
[6] Bronsted; Rockafellar: On the subdifferentiability of convex functions. Proc. AMS 16, 605-611 (1965) · 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. Proc. symp. Pure math. 15 (1968) · Zbl 0217.20601
[9] Ebin: Espace des métriques riemanniennes et mouvement des fluides via LES variétés d’applications. Lecture notes (1971--1972)
[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)
[15] Eliasson: Variation integrals in fiber bundles. Global analysis, proc. Symp. pure math. AMS 16 (1968)
[16] Grossmann: Geodesics on Hilbert manifolds. Ph.d. thesis (1964) · Zbl 0144.23603
[17] Krasnoselski: Topological methods in the theory of nonlinear integral equations. (1963)
[18] Lang: Differential manifolds. (1970)
[19] Macalpin: Infinite dimensional manifolds and Morse theory. Ph.d. thesis (1965)
[20] Palais: Foundations of global nonlinear analysis. (1968)
[21] Palais: Banach manifolds of fibre bundle sections. Congrès int. Des mathématiciens (1970)
[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)
[25] Penot: Diverses méthodes de construction de variétés d’applications. Thesis (1970)
[26] Penot: Topologie faibles sur des variétés de Banach application aux géodésiques des variétés de Sobolev. (1972)
[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)