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

摘要

In this paper we study the existence of positive large solutions for the equation Δ_pu+λ|Δu|p-1=p(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.