Lower order term for the fractional Laplacian with a Hardy potential

This paper is concerned with the following semilinear elliptic equation involving the fractional Laplacian: (-Δ)ˢ u+ g|u|ᵖ⁻¹u= λu|x|²ˢ+f(x), in a bounded domain $Ω$ of RN\,(N>2s), subject to the zero Dirichlet condition in RN Ω, where $0 1$ and f∈ L(p+1)/pg(Ω). Under certain integrability condition on g, the existence of solution is proven for every λ∈ R. Moreover, the regularity of solution is also obtained.