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DCDS

We deal with indefinite Lagrangian systems of the form

$ x''+\partial_{x}V(x,y)=0,\ x\in R^{n};\qquad \ -y''+\partial_{y}V(x,y)=0,\ y\in R^{m}, $

where $V\in C^{1}(R^{n+m},R)$. We are interested in the existence of a brake periodic orbit of prescribed Hamiltonian. This problem may be considered as a generalization of the classical case $m=0$, for which are known many existence results (Seifert theorem and its developments), and also a generalization of the case $n=1$, whose study has been initiated by Hofer and Toland and which is still under investigation. Here we assume at least a quadratic growth on $V$ in order to find a brake orbit via a linking variational principle.

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