Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit

@article{Hu2018MorseIT,
  title={Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit},
  author={Xijun Hu and Li Wu and Ran Yang},
  journal={Journal of Dynamics and Differential Equations},
  year={2018},
  volume={32},
  pages={61-84}
}
In this paper, we prove Morse index theorem of Lagrangian systems with self-adjoint boundary conditions. Based on it, we give some nontrivial estimates on the difference of Morse indices. As an application, we get a new criterion for the stability problem of brake periodic orbit. 
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