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In this paper, we consider the indefinite fractional elliptic problem. Acorresponding Liouville-type theorem for the indefinite fractional ellipticequations is established. Furthermore, we obtain a priori bound for solutionsin a bounded domain by blowing-up and re-scaling. We also classify thesolutions of some degenerate elliptic equation originated from fractionalLaplacian.

Indefinite fractional elliptic problem and Liouville theorems