A Remark on the Existence of Positive Solutions for Some Elliptic Systems

In this paper we study the existence of positive solutions for the system where Δ is the Laplacian operator, λ is a real positive parameter, Ω is a bounded domain in R^N (N ≥ 1) with smooth boundary ∂Ω, and f, g are C¹ functions satisfying uniformly in σ uniformly in x, and uniformly in x. In particular we do not assume any sign conditions on f(x, 0, 0) or g(x, 0, 0) for all x ∈ Ω. For λ large we prove the existence of a large positive solution. Our approach is based on the method of subsuper solutions.