Large solutions for a class of semilinear integro-differential equations with censored jumps

We study existence of large solutions, that is, solutions that verify u(x)→+∞u(x)→+∞ as x→∂Ωx→∂Ω, for equations like−I(u,x)+u(x)p=0,x∈Ω, where Ω is a bounded smooth domain in RNRN, p>1p>1 and II is a nonlocal operator of the formI(u,x)=P.V.∫|z|≤ϱ(x)[u(x+z)−u(x)]|z|−(N+α)dz, where α∈(0,2)α∈(0,2) and ϱ:Ω¯→R is a function whose main particularity is that 0<ϱ(x)≤dist(x,∂Ω)0<ϱ(x)≤dist(x,∂Ω). We also obtain uniqueness of the solution in a class of large solutions whose blow-up rate depends on p,αp,α and the rate at which ϱ shrinks near the boundary.