ABSTRACT
This chapter refines the classical a priori bounds of J. B. Keller [123] and R. Osserman [202] to establish the existence of a minimal and a maximal positive solution for the singular boundary value problem{ −d∆u = λu+ a(x)f(x, u)u in D,
u =∞ on ∂D, (3.1)
under condition (KO). As a byproduct, it will become apparent that
θ[λ,D,∞] := lim M↑∞
θ[λ,D,M ] (3.2)
provides us with the minimal positive solution of (3.1), where θ[λ,D,M ] stands for the unique positive solution of (2.2).
