  The Fujita phenomenon for nonlinear parabolic problems dtu = \deltau + up in
an exterior domain of RN under the Robin boundary conditions is investigated in
the superlinear case. As in the case of Dirichlet boundary conditions, it turns
out that there exists a critical exponent p = 1+2/N such that blow-up of
positive solutions always occurs for subcritical exponents, whereas in the
supercritical case global existence can occur for small non-negative initial
data.
