Radial solutions of p-Laplace equations with nonlinear gradient terms on exterior domains

This paper studies the existence of radial solutions of the boundary value problem of p -Laplace equation with gradient term { − Δ p u = K ( | x | ) f ( | x | , u , | ∇ u | ) , x ∈ Ω , ∂ u ∂ n = 0 , x ∈ ∂ Ω , lim | x | → ∞ u ( x ) = 0 , where Ω = { x ∈ R N : | x | > r 0 } , N ≥ 3 , 1 < p ≤ 2 , K : [ r 0 , ∞ ) → R + , and f : [ r 0 , ∞ ) × R × R + → R are continuous. Under certain inequality conditions of f , the existence results of radial solutions are obtained.