General uniqueness results

This chapter establishes the uniqueness of the positive solution of the singular boundary value problem −d∆u = λu+ a(x)g(u)u in Ωj ,u = 0 on ∂Ωj ∩ ∂Ω,

u =∞ on ∂Ωj \ ∂Ω, (8.1)

under the following assumptions:

(i) d > 0, λ ≥ 0, and a(x) satisfies Hypothesis (Ha). (ii) g ∈ C[0,∞) ∩ C1(0,∞) satisfies (7.2), (7.10) and (7.16).