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| Brake Subharmonic Solutions of Subquadratic Hamiltonian Systems |
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Citation： |
C. Li.Brake Subharmonic Solutions of Subquadratic Hamiltonian Systems[J].Chinese Annals of Mathematics B,2016,37(3):405~418 |
| Page view： 1381
Net amount： 991 |
Authors： |
C. Li; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11501030, 11226156) and the Beijing
Natural Science Foundation (No.1144012). |
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| Abstract： |
The author mainly uses the Galerkin approximation method and the
iteration inequalities of the $L$-Maslov type index theory to study
the properties of brake subharmonic solutions for the Hamiltonian
systems $\dot{z}(t)=J\nabla H(t,z(t))$, where $H(t,z)=\frac{1}{2}
(\wh{B}(t)z,z)+\wh{H}(t,z)$, $\wh{B}(t)$ is a semipositive symmetric
continuous matrix and $\wh{H}$ is unbounded and not uniformly
coercive. It is proved that when the positive integers $j$ and $k$
satisfy the certain conditions, there exists a $jT$-periodic
nonconstant brake solution $z_{j}$ such that $z_{j}$ and $z_{kj}$
are distinct. |
Keywords： |
Brake subharmonic solution, $L$-Maslov type index, Hamiltonian
systems |
Classification： |
58E05, 34C25, 70H05 |
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