\`x^2+y_1+z_12^34\`
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Existence and decay property of ground state solutions for Hamiltonian elliptic system

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This work was supported by the NNSF (Nos. 11701173, 11601145, 11571370, 61772196), by the Natural Science Foundation of Hunan Province (Nos. 2017JJ3130, 2017JJ3131), by the Excellent youth project of Education Department of Hunan Province (17B143), by the Hunan University of Commerce Innovation Driven Project for Young Teacher (16QD008), and by the Project funded by China Postdoctoral Science Foundation (2018M640758)

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