Abstract
In this paper, we study the multiplicity problem for Euler–Lagrange orbits that satisfy the conormal boundary conditions for a suitable class of reversible Lagrangian functions on compact manifolds. Such a class contains, e.g. the energy function of reversible Finsler metrics that satisfy a convexity condition on the boundary.
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Notes
Two curves \(\gamma _1,\gamma _2: [0,1] \rightarrow {\overline{\Omega }}\) are considered distinct if \(\gamma _1([0,1]) \ne \gamma _2([0,1])\).
There is a standard construction of metrics for which a given closed embedded submanifold of a differentiable manifold is totally geodesic. Such metrics are constructed in a tubular neighbourhood first, using a normal bundle construction, and then extended using a partition of unity argument.
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Corona, D. A multiplicity result for Euler–Lagrange orbits satisfying the conormal boundary conditions. J. Fixed Point Theory Appl. 22, 60 (2020). https://doi.org/10.1007/s11784-020-00795-4
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DOI: https://doi.org/10.1007/s11784-020-00795-4