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

• Published in: Asymptotic analysis Vol. 46; no. 3-4; pp. 275 - 298
• Main Authors: Cîrstea, Florica Corina, Rădulescu, Vicenţiu
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.03.2006
• ISSN: 0921-7134; 1875-8576
• DOI: 10.3233/ASY-2006-732

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.