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By using the abstract version of Struwe's monotonicity-trick we prove theexistence of a positive solution to the problem (-\Delta)^s u + K u = f(x, u)in R^N u\in H^s (R^N), K>0 where f(x, t): R^N\times R \rightarrow R is aCaratheodory function, 1-periodic in x and does not satisfy theAmbrosetti-Rabinowitz condition.

A fractional Landesman-Lazer type problem set on R^N