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First integrals for problems of calculus of variations on locally convex spaces. (English) Zbl 1198.49019

The fundamental problem of calculus of variations is considered when solutions are differentiable curves on locally convex spaces. Such problems admit an extension of the Euler-Lagrange equations [I. V. Orlov, Cybern. Syst. Anal. 38, No. 4, 493–502 (2002); translation from Kibern. Sist. Anal. 2002, No. 4, 24–35 (2002; Zbl 1029.46127)] for continuously normally differentiable Lagrangians. Here, we formulate a Legendre condition and an extension of the classical theorem of Emmy Noether, thus obtaining first integrals for problems of the calculus of variations on locally convex spaces.

MSC:

49K27 Optimality conditions for problems in abstract spaces
46T20 Continuous and differentiable maps in nonlinear functional analysis
47J30 Variational methods involving nonlinear operators
49K05 Optimality conditions for free problems in one independent variable
58E30 Variational principles in infinite-dimensional spaces

Citations:

Zbl 1029.46127
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