We study nonnegative solutions of the equationut=2u+a(x) upinRd,t>0, under the assumption thata(x) 0 is on the order xm, form (−2, ∞), or that 0 a(x) Cx−2. Extending the classical result of Fujita and more recent results of Bandle and Levine and of Levine and Meier, we find a critical exponentp*=p*(m, d) such that if 1
p*, then there exist both global and nonglobal solutions.
