Nonlinear problems with boundary blow-up: a Karamata regular variation theory approach

Article type: Research Article

Authors: Cîrstea, Florica Corina | Rădulescu, Vicenţiu

Affiliations: Department of Mathematics, Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200, Australia E-mail: [email protected] | Department of Mathematics, University of Craiova, 13 A.I. Cuza Street, 200585 Craiova, Romania E-mail: [email protected]

Abstract: We study the uniqueness and expansion properties of the positive solution of the logistic equation Δu+au=b(x)f(u) in a smooth bounded domain Ω, subject to the singular boundary condition u=+∞ on $\curpartial \varOmega $. The absorption term f is a positive function satisfying the Keller–Osserman condition and such that the mapping f(u)/u is increasing on (0,+∞). We assume that b is non-negative, while the values of the real parameter a are related to an appropriate semilinear eigenvalue problem. Our analysis is based on the Karamata regular variation theory.

Journal: Asymptotic Analysis, vol. 46, no. 3-4, pp. 275-298, 2006