Abstract
We study nonnegative solutions of the equationut=2u+a(x)upinRd,t>0, under the assumption thata(x)≩0 is on the order |x|m, form∈(−2,∞), or that 0≨a(x)⩽C|x|−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⩽p*, then there exist no solutions that are global in time, while ifp>p*, then there exist both global and nonglobal solutions.
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