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The Morse index theorem for regular Lagrangian systems
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.