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In the following, we show the strong comparison principle for the fractional p-Laplacian, i.e. we analyze

We study solutions of the problem 0.1−(−Δ)α/2u=f(x,u)inD0∖D¯1,u=0inRN∖D0,u=1inD¯1, where D1,D0⊂RN are open sets such that D¯1⊂D0, α∈(0,2), and f is a nonlinearity. Under different assumptions on f we prove that, if D0 and D1 are starshaped with respect to the same point x¯∈D¯1, then the same occurs for every superlevel set of u. [ABSTRACT FROM AUTHOR]