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Subharmonic solutions and minimal periodic solutions of first-order Hamiltonian systems with anisotropic growth

  • * Corresponding author: Chungen Liu

    * Corresponding author: Chungen Liu 
The first author is supported partially by the NSF of China (11071127,10621101), 973 Program of MOST (2011CB808002) and SRFDP.
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  • Using a homologically link theorem in variational theory and iteration inequalities of Maslov-type index, we show the existence of a sequence of subharmonic solutions of non-autonomous Hamiltonian systems with the Hamiltonian functions satisfying some anisotropic growth conditions, i.e., the Hamiltonian functions may have simultaneously, in different components, superquadratic, subquadratic and quadratic behaviors. Moreover, we also consider the minimal period problem of some autonomous Hamiltonian systems with anisotropic growth.

    Mathematics Subject Classification: 35F60, 53D12, 58E05.


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