The boundary blow-up rate of large solutions

[摘要] In this paper we ascertain the blow-up rate of the large solutions of a class of sublinear elliptic boundary value problems with a weight function in front of the nonlinearity that vanishes on the boundary of the underlying domain, Omega, at different rates according to the point of the boundary, x(x) is an element of partial derivativeOmega. All previous results in the literature assumed the decay rate of the underlying weight function to be the same at any point of partial derivativeOmega. This hypothesis substantially simplified the mathematical analysis of the problem, as it allowed constructing global sub and supersolutions in an open neighborhood of partial derivativeOmega. Obtaining general results requires localizing at each particular point of the boundary, making particularly involved the mathematical analysis of the problem. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-11-20

[关键词] large solutions;vanishing weight at variable rates;blowing-up rates