Classical and weak solutions of a singular semilinear elliptic problem

[摘要] The singular semilinear elliptic equation Delta u + p(x)f(u) = 0 is shown to have a unique positive classical solution in R-n that decays to zero at infinity if p(x) is simply a nontrivial nonnegative continuous function satisfying integral(0)(infinity) t max(\x\=t) p(x) dt < infinity provided f is a non-increasing continuously differentiable function on (0, infinity). It is also shown that the equation has a unique weak H-0(1)-solution on a bounded domain provided integral(0)(epsilon) f(s) ds < infinity and p(x) is an element of L-2. (C) 1997 Academic Press.

[发布日期] 1997-07-15