On the existence of ground states of nonlinear fractional Schrödinger systems with close-to-periodic potentials

We are concerned with the nonlinear fractional Schrodinger system {(-Delta)(s)u + V-1(x)u = f (x, u) + Gamma (x) vertical bar u vertical bar (q-2) u vertical bar upsilon vertical bar(q) in R-N, (-Delta)(s)u + V-2(x)u = g (x, upsilon) + Gamma (x) vertical bar upsilon vertical bar (q-2) upsilon vertical bar upsilon vertical bar(q) in R-N, u, upsilon is an element of H-s (R-N), where (-Delta)(s) is the fractional Laplacian operator, s is an element of(0, 1), N > 2s, 4 <= 2q < p < 2*, 2* = 2 N/(N - 2 s). V-i (x) = V-per(i) (x) + V-loc(i) (x) is closed-to-periodic for i - 1, 2, f and g have subcritical growths and Gamma(x) >= 0 vanishes at infinity. Using the Nehari manifold minimization technique, we first obtain a bounded minimizing sequence, and then we adopt the approach of Jeanjean-Tanaka [8] to obtain a decomposition of the bounded Palais-Smale sequence. Finally, we prove the existence of ground state solutions for the nonlinear fractional Schrodinger system.