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Zbl 1039.35036
Chuaqui, M.; Cortázar, C.; Elgueta, M.; Flores, C.; Letelier, R.; Garc\'ia-Melián, J.
On an elliptic problem with boundary blow-up and a singular weight: the radial case. (English)
[J] Proc. R. Soc. Edinb., Sect. A, Math. 133, No. 6, 1283-1297 (2003). ISSN 0308-2105; ISSN 1473-7124/e

The authors study a semilinear elliptic problem with boundary blow-up of the form $$ \Delta u=a(x)u^m\quad \text{ in}\ \Omega,\quad u=+\infty\quad \text{ on}\ \partial\Omega. $$ Assuming that $a$ is a continuous radial function with $a(x)\sim C_0\text{ dist\,}(x,\partial B)^{-\gamma}$ as\par $\text{ dist\,}(x,\partial B)\to 0,$ for some $C_0>0,$ $\gamma>0,$ the authors determine the issues of existence, multiplicity and behaviour near the boundary for radial positive solutions, in terms of the values of $m$ and $\gamma.$ The case $0<m\leq 1,$ as well as estimates for solutions to the linear problem $m=1$ are also considered.
[Lubomira Softova (Bari)]

MSC 2000:: *35J60 Nonlinear elliptic equations
35B45 A priori estimates
35J25 Second order elliptic equations, boundary value problems

Keywords: semilinear elliptic equations; boundary blow-up; radial positive solutions

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Zentralblatt MATH Berlin [Germany]