GROUND STATE SOLUTION FOR A CLASS FRACTIONAL HAMILTONIAN SYSTEMS

In this paper, we consider a class of Hamiltonian systems of the form tD α ∞(−∞D α t u(t)) + L(t)u(t)−∇W (t, u(t)) = 0 where α ∈ ( 1 2 , 1), −∞D α t and tD α ∞ are left and right Liouville-Weyl fractional derivatives of order α 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, ConcentrationCompactness Principle and a new form of Lions Lemma respect to fractional differential equations.