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

Florica Corina Cirstea·Vicentiu Radulescu
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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 $u=+\infty$ on $\partialΩ$. The absorption term $f$ is a positive function satisfying the Keller--Osserman condition and such that the mapping $f(u)/u$ is increasing on $(0,+\infty)$. 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.

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Florica Corina Cirstea, Vicentiu Radulescu. 2005-06-07. Nonlinear problems with boundary blow-up: a Karamata regular variation theory approach. https://arxiv.org/abs/math/0506122

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