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Volume 8, Number 2, 2018, Pages 620-648                                                                DOI:10.11948/2018.620
Ground state solution for a class fractional Hamiltonian systems
Ying Lv,Chunlei Tang and Boling Guo
Keywords:Fractional Hamiltonian systems, ground state, local mountain pass theorem, concentration-compactness principle.
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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