Cîrstea, Florica-CorinaRădulescu, Vicenţiu2016-03-152016-03-150002-9947http://hdl.handle.net/1885/100254We establish the uniqueness of the positive solution for equations of the form −∆u = au − b(x)f(u) in Ω, u|∂Ω = ∞. The special feature is to consider nonlinearities f whose variation at infinity is not regular (e.g., exp(u) − 1, sinh(u), cosh(u) − 1, exp(u) log(u + 1), uᵝ exp(uᵞ), β ∈ R, γ > 0 or exp(exp(u)) − e) and functions b ≥ 0 in Ω vanishing on ∂Ω. The main innovation consists of using Karamata’s theory not only in the statement/proof of the main result but also to link the nonregular variation of f at infinity with the blow-up rate of the solution near ∂Ω.The research of the first author was carried out at Victoria University (Melbourne) with the support of the Australian Government through DETYA. The second author has been supported by Grant 2-CEX06-11-18/2006.© 2007 American Mathematical SocietyLarge solutionsboundary blow-upregular variation theory2007-02-1310.1090/S0002-9947-07-04107-42016-06-14