The asymptotic behaviour of the unique solution for the singular Lane-Emden-Fowler equation

[摘要] By Karamata regular variation theory and constructing comparison functions, we show the exact asymptotic behaviour of the unique classical solution u is an element of C-2(Omega) boolean AND C((Omega) over bar) near the boundary to a singular Dirichlet problem -Delta u = k(x)g(u), u > 0, x is an element of Omega, u vertical bar(partial derivative Omega) = 0, where Omega is a bounded domain with smooth boundary in R-N; g is an element of C-1 ((0, infinity), (0, infinity)), liM(t -> 0)+ g(xi t)/g(t) = xi(-gamma) for each xi > 0, for some gamma > 0; and k is an element of C-loc(alpha)(Omega) for some alpha is an element of (0, 1), is nonnegative on Omega, which is also singular near the boundary. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2005-12-01

[关键词] semilinear elliptic equations;Dirichlet problem;singularity;Karamata regular variation theory;unique solution;existence;exact asymptotic behaviour