The paper deals with the nonnegative solutions to the Cauchy problem
where and is of order for or Extending the classical result of H. Fujita [J. Fac. Sci., Univ. Tokyo, Sect. I 13, 109-124 (1966; Zbl 0163.34002)] and more recent results of C. Bandle and H. A. Levine [Trans. Am. Math. Soc. 316, No. 2, 595-622 (1989; Zbl 0693.35081)] and H. A. Levine and P. Meier [Arch. Ration. Mech. Anal. 109, No. 1, 73-80 (1990; Zbl 0702.35131)], the author finds a critical exponent such that if then there exist no solutions to that are global in time, while if then there exist both global and nonglobal solutions.