The boundary blow-up rate of large solutions

Abstract 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, Ω , at different rates according to the point of the boundary, x ∞ ∈∂Ω . All previous results in the literature assumed the decay rate of the underlying weight function to be the same at any point of ∂Ω . This hypothesis substantially simplified the mathematical analysis of the problem, as it allowed constructing global sub and supersolutions in an open neighborhood of ∂Ω . Obtaining general results requires localizing at each particular point of the boundary, making particularly involved the mathematical analysis of the problem.

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