Existence of blow-up solutions for a non-linear equation with gradient term in

In this paper we study the existence of positive large solutions for the equation Δ p u + λ | ∇ u | p − 1 = ρ ( x ) f ( u ) in R N , where f is a non-negative non-decreasing function and ρ is a non-negative continuous function. We show under some hypotheses detailed below the existence of positive solutions which blow up at infinity.