Blow-up solutions to a -Laplacian system with gradient term

In this work, we are mainly concerned with the existence and non-existence of blow-up positive solutions for the nonlinear system Δ p u + λ ( | x | ) | ∇ u | p − 1 = ϕ ( | x | ) f ( v ) , Δ q v + μ ( | x | ) | ∇ v | q − 1 = ψ ( | x | ) g ( u ) in R N . Sufficient conditions for the existence and non-existence of blow-up solutions are established.