A remark on the existence of entire solutions of a singular semilinear elliptic problem

[摘要] It is proved that the singular semilinear elliptic equation -Delta u = p(x)g(u), 0 less than or equal to p(x), x epsilon R-n, 2 less than or equal to n, lim (s --> 0) + g(s) = +infinity, and g epsilon C-1 ((0, infinity), (0, infinity)) which is strictly decreasing in (0, infinity), has a unique positive C-loc(2+alpha)(R-n) solution that decays to zero near infinity provided integral(0)(infinity) t phi(t)dt < infinity, where phi(t) = max (\x\=t) g(x). (C) 1997 Academic Press.

[发布日期] 1997-11-15