Large solutions to elliptic equations involving fractional Laplacian

The purpose of this paper is to study boundary blow up solutions for semi-linear fractional elliptic equations of the formequation(0.1){(−Δ)αu(x)+|u|p−1u(x)=f(x),x∈Ω,u(x)=0,x∈Ω¯c,limx∈Ω,x→∂Ω⁡u(x)=+∞, where p>1p>1, Ω   is an open bounded C2C2 domain of RNRN, N≥2N≥2, the operator (−Δ)α(−Δ)α with α∈(0,1)α∈(0,1) is the fractional Laplacian and f:Ω→Rf:Ω→R is a continuous function which satisfies some appropriate conditions. We obtain that problem (0.1) admits a solution with boundary behavior like d(x)−2αp−1, when 1+2α