Existence of positive solutions to fractional elliptic problems with Hardy potential and critical growth.

In this work, we study the following critical problem involving the fractional Laplacian: (−Δ)su−μu|x|2s=λg(x)up+K(x)u2s∗−1,x∈RN,where s  ∈  (0,1), N  >  2s, 0<p<2s∗−1, and 2s∗=2NN−2s is the fractional critical exponent, 0  <  μ  <  ΛN,s, the sharp constant of the Hardy‐Sobolev inequality. For suitable assumptions on g(x) and K(x), we consider the existence and multiplicity of positive solutions depending on the value of p. Moreover, we obtain an existence result for the problem when λ  =  0. [ABSTRACT FROM AUTHOR]