Existence and uniqueness of nonnegative solutions for a boundary blow-up problem

Assume that Ω is a bounded domain in R N ( N ⩾ 3 ) with smooth boundary ∂Ω. In this work, we study existence and uniqueness of blow-up solutions for the problem − Δ p ( u ) + c ( x ) | ∇ u | p − 1 + F ( x , u ) = 0 in Ω, where 2 ⩽ p . Under some conditions related to the function F, we give a sufficient condition for existence and nonexistence of nonnegative blow-up solutions. We study also the uniqueness of these solutions.