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)→+ ∞ as x→ ∂. Ω, for equations like. -I(u,x)+u(x)p= 0,x∈Ω, where Ω is a bounded smooth domain in RN, p> 1 and I is a nonlocal operator of the form, where α. ∈ (0, 2) and ρ:Ω-→R is a function whose main particularity is that 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, α and the rate at which ρ shrinks near the boundary. © 2016 Elsevier Inc.