| Nontrivial Solutions of Superquadratic Hamiltonian Systems with Lagrangian Boundary Conditionsand the L-index Theory |
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| 作者单位： | Chong LI Chungen LIU School of Mathematical Sciences，Nankai University，Tianjin 300071，China.School of Mathematical Sciences and LPMC，Nankai University，Tianjin 300071，China. |
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| 基金项目： | 国家自然科学基金，国家重点基础研究发展计划(973计划) |
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| 摘 要： | In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z(t) = JH(t,z(t)) with Lagrangian boundary conditions, where H(t,z)=1/2((B)(t)z,z) (H)(t,z),(B)(t) is a semipositive symmetric continuous matrix and (H) satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.
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Nontrivial Solutions of Superquadratic Hamiltonian Systems with Lagrangian Boundary Conditions and the L-index Theory |
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| Authors: | Chong LI Chungen LIU |
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| Abstract: | In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z(t) = J▽H(t, z(t)) with Lagrangian boundary conditions, where (H)(t,z) = 1/2((B)(t)z,z) (H)(t,z), (B)(t) is a semipositive symmetric continuous matrix and (H) satisfies a superquadratic condition at infinity. We also obtain a result about the L-index. |
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| Keywords: | L-index Nontrivial solution Hamiltonian systems Lagrangian boundary conditions Superquadratic condition |
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