Received 23 December 1998. 

Available online 25 March 2002.

Abstract

We study the problem

u ≥ 0 in Ω,where Ω is an unbounded domain with smooth boundary Γ, n denotes the unit outward normal vector on Γ, and λ > 0, θ are real parameters. We assume throughout that , while a, b, and h are positive functions. We show that there exist an open interval I and λ* > 0 such that the problem has no solution if θ  I and λ  (0, λ*). Furthermore, there exist an open interval J  I and λ₀ > 0 such that, for any θ  J, the above problem has at least a solution if λ ≥ λ₀, but it has no solution provided that λ  (0, λ₀). Our paper extends previous results obtained by J. Chabrowski and K. Pflüger.