Finite reduction and Morse index estimates for mechanical systems

Details Finite reduction and Morse index estimates for mechanical systems Finite reduction and Morse index estimates for mechanical systems

2010-04-07

arxiv.org/abs/1004.1133v2

NoDEA : Nonlinear Differential Equations and Applications (9 March 2011), pp. 1-13

Physics

Mathematical Physics

13 pages; v2: minor changes, to appear in Nonlinear Differential Equations and Applications

Scientific paper

10.1007/s00030-011-0107-4

A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.

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