Abstract

In this work we consider the non-autonomous problem ?u = a(x)u m in the unit ball B ? ?N, with the boundary condition u|?B = +?, and m > 0. Assuming that a is a continuous radial function with a(x) ? C0 dist(x, ?B) -? as dist(x, ? B) ? 0, for some C0 > 0, ? > 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 ?. The case 0 < m ? 1, as well as estimates for solutions to the linear problem m = 1, are a significant part of our results.