Classical and Weak Solutions of a Singular Semilinear Elliptic Problem

AbstractThe singular semilinear elliptic equation Δu+p(x)f(u)=0 is shown to have a unique positive classical solution inRnthat decays to zero at ∞ ifp(x) is simply a nontrivial nonnegative continuous function satisfying ∫∞0tmax|x|=tp(x)dt<∞, providedfis a non-increasing continuously differentiable function on (0,∞). It is also shown that the equation has a unique weakH10-solution on a bounded domain provided ∫ε0f(s)ds<∞ andp(x)∈L2