Ground state solution for a class fractional Hamiltonian systems |
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Authors: | Ying Lv Chunlei Tang and Boling Guo |
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Institution: | School of Mathematics and Statistics, Southwest University, Chongqing 400715, People''s Republic of China,School of Mathematics and Statistics, Southwest University, Chongqing 400715, People''s Republic of China,Institute of Applied Physics and Computational Mathematics, Beijing 100094, People''s Republic of China |
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Abstract: | In this paper, we consider a class of Hamiltonian systems of the form $_tD_\infty^\alpha(_{-\infty} D_t^\alpha u(t))+L(t) u(t)-\nabla W(t,u(t))=0$ where $\alpha\in(\frac{1}{2},1)$, $_{-\infty}D_t^\alpha$ and $_{t}D_\infty^\alpha$ are left and right Liouville-Weyl fractional derivatives of order $\alpha$ on the whole axis $R$ respectively. Under weaker superquadratic conditions on the nonlinearity and asymptotically periodic assumptions, ground state solution is obtained by mainly using Local Mountain Pass Theorem, Concentration-Compactness Principle and a new form of Lions Lemma respect to fractional differential equations. |
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Keywords: | Fractional Hamiltonian systems ground state local mountain pass theorem concentration-compactness principle |
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