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| Nontrivial Solutions of Superquadratic Hamiltonian systems with Lagrangian Boundary Conditions and the L-index Theory |
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Citation： |
Chong LI,Chungen LIU.Nontrivial Solutions of Superquadratic Hamiltonian systems with Lagrangian Boundary Conditions and the L-index Theory[J].Chinese Annals of Mathematics B,2008,29(6):597~610 |
| Page view： 1140
Net amount： 799 |
Authors： |
Chong LI; Chungen LIU |
Foundation： |
Partially supported by the National Natural Science Foundation of China (Nos. 10531050, 10621101) and the 973 Project of the Ministry of Science and Technology of China. |
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| Abstract： |
In this paper, the authors study the existence of nontrivial solutions for the
Hamiltonian systems$\dot z(t)=J\na H(t,z(t))$with Lagrangian boundary conditions, 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 $\wh H$
satisfies a superquadratic condition at infinity. We also obtain a result about the L-index. |
Keywords： |
L-index, Nontrivial solution, Hamiltonian systems, Lagrangian boundary conditions, Superquadratic condition |
Classification： |
58F05, 58E05, 34C25, 58F10 |
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