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MiS Preprint
55/2003

The Morse index theorem for regular Lagrangian systems

Chaofeng Zhu

Abstract

In this paper, we prove the Morse index theorem for the index forms of regular Lagrangian systems with selfadjoint boundary condition coming from variational problems. We then give the relationship of them under two different boundary conditions. The Morse index theorem for the corresponding second order selfadjoint differential operators will be proved in recent paper: B. Booss and C. Zhu, The general spectral flow formula.

Received:
Jul 1, 2003
Published:
Jul 1, 2003
MSC Codes:
34B05, 53C22, 58C50, 58E10, 70H05
PACS:
02.40
Keywords:
regular lagrangian system, index form, spectral flow, relative morse index, maslov index, maslov-type index

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Preprint
2003 Repository Open Access
Chaofeng Zhu

The Morse index theorem for regular Lagrangian systems