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

Abstract:

In this work we consider the non-autonomous problem u = a(x)u^m in the unit ball B R^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.

Document Type: Research article

Publication date: 2003-12-19

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