Nonlinear problems with boundary blowup: a Karamata regular variation theory approach
Abstract
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 KellerOsserman condition and such that the mapping $f(u)/u$ is increasing on $(0,+\infty)$. We assume that $b$ is nonnegative, 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2005
 DOI:
 10.48550/arXiv.math/0506122
 arXiv:
 arXiv:math/0506122
 Bibcode:
 2005math......6122C
 Keywords:

 Mathematics  Analysis of PDEs