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In this paper we consider the existence and regularity of solutions to the following nonlocal Dirichlet problems: $$ textstylebegin{cases} (-Delta)^{s} u-lambdafrac{u}{|x|^{2s}}+u^{p}=f(x), u0026xinOmega,  uu003e0, u0026xinOmega,  u=0, u0026 xinmathbb{R}^{N}setminusOmega, end{cases} $$where ((-Delta)^{s}) is the fractional Laplacian operator, (sin(0,1)), (Omegasubsetmathbb{R}^{N}) is a bounded domain with Lipschitz boundary such that (0inOmega), f is a nonnegative function that belongs to a suitable Lebesgue space.

Combined effects of the Hardy potential and lower order terms in fractional Laplacian equations