On an elliptic problem with boundary blow-up and a singular weight: the radial case

Authors: Chuaqui M.; Cortázar C.; Elgueta M.; Flores C.; Letelier R.; García-Melián J.

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 133, Number 6, 19 December 2003 , pp. 1283-1297(15)

Publisher: Royal Society of Edinburgh

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Abstract:

In this work we consider the non-autonomous problem Deltau = a(x)um in the unit ball B sub RN, with the boundary condition u|partB = +infin, and m > 0. Assuming that a is a continuous radial function with a(x) ~ C0 dist(x, partB)-gamma as dist(x, partB) rarr 0, for some C0 > 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 le 1, as well as estimates for solutions to the linear problem m = 1, are a significant part of our results.

Document Type: Research article

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