A Uniqueness Result for a Singular Nonlinear Eigenvalue Problem

We consider the positive solutions to singular boundary-value problems of the form where λ \u3e 0, β ∈ (0,1) and Ω is a bounded domain in ℝ N , N ≥ 1, with smooth boundary ∂Ω. Here, we assume that f: [0, ∞) → (0, ∞) is a C 1 non-decreasing function and f(s)/s β is decreasing for s large. We establish the uniqueness of the positive solution when λ is large