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On an elliptic problem with boundary blow-up and a singular weight: the radial case. (English) Zbl 1039.35036

The authors study a semilinear elliptic problem with boundary blow-up of the form

Δu=a(x)u m inΩ,u=+onΩ·

Assuming that a is a continuous radial function with a(x)C 0 dist(x,B) -γ as

dist(x,B)0, for some C 0 >0, γ>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 γ· The case 0<m1, as well as estimates for solutions to the linear problem m=1 are also considered.

MSC:
35J60Nonlinear elliptic equations
35B45A priori estimates for solutions of PDE
35J25Second order elliptic equations, boundary value problems