  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 [Orlov 2002] 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.
