Nonlocal elliptic equations involving measures

In this article, we study the existence of solution for the problem (−Δ)αu=λf(u)+ν(−Δ)αu=λf(u)+ν in Ω, u≡0u≡0 in RN\ΩRN\Ω, where λ>0λ>0 is a parameter, α∈(0,1)α∈(0,1) and ν is a Radon measure. A weak solution is obtained by using Schauder's fixed point theorem. In the case where ν is Dirac measure, the symmetry of the solution is obtained by using the moving plane method.