On an elliptic problem with boundary blow-up and a singular weight
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Date
2003
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Abstract
In this work we consider the non-autonomous problem Deltau = a(x)u(m) in the unit ball B subset of R-N, with the boundary condition u\(partial derivativeB) = +infinity, and m > 0. Assuming that a is a continuous radial function with a(x) similar to C-0 dist(x, partial derivativeB)(-gamma) as dist(x, partial derivativeB) --> 0, for some C-0 > 0, gamma > 0, we completely 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 less than or equal to 1, as well as estimates for solutions to the linear problem m = 1, are a significant part of our results.