PERIODIC SOLUTIONS FOR THE NON-LOCAL OPERATOR (-Δ plus m2)s - m2s WITH m ≥ 0

By using variational methods, we investigate the existence of T-periodic solutions to {[(-Delta(x) + m(2))(s) - m(2s)]u = f(x, u) in (0, T)(N), u(x + Te-i) = u(x) for all x is an element of R-N, i = 1 , . . . ,N, where s is an element of(0, 1), N > 2s, T > 0, m >= 0 and f is a continuous function, T-periodic in the first variable, verifying the Ambrosetti-Rabinowitz condition, with a polynomial growth at rate p is an element of(1, (N 2s)/(N 2s)).