正定型超曲面上Hamilton系统Brake轨道的存在性

Existence of Brake orbit of Hamiltonian systems on positivetype hypersurfaces

结合Rabinowitz和Szulkin关于Brake轨道的存在性与多重性的结论,利用部分对称泛函的临界点理论研究Hamilton系统在更广泛的能量面上Brake轨道的存在性问题.在适当条件下,证明了R2n中正定型超曲面Σ上存在Hamilton系统的Brake轨道.由于星型超曲面是正定型超曲面的特殊情形,该研究包含了Rabinowitz的相应结论.

In combination with the conclusion about the existence and multiplicity of Brake orbit, which was obtained by Rabinowitz and Szulkin, a study was made on the existence of Brake Orbit of Hamiltonian systems on a more general energy hypersurface by use of the critical point theory of partial symmetric functionals. The existence of Brake orbit of Hamiltonian systems on positive-type hypersurface ∑ with partial symmetry in R^2n was verified under certain conditions. Since the star-shaped hypersurface is a special case of positive-type hypersurfaces, the present study extends the reseawh work of P. Rabinowitz in 1987.