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

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

2005-06-07

arxiv.org/abs/math/0506122v1

Mathematics

Analysis of PDEs

Scientific paper

We study the uniqueness and expansion properties of the positive solution of the logistic equation $\Delta u+au=b(x)f(u)$ in a smooth bounded domain $\Omega$, subject to the singular boundary condition $u=+\infty$ on $\partial\Omega$. 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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