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This paper deals with a Cauchy problem of the inhomogeneous parabolic, where constants γ > 0, p > 1, and σ > À 1. The Japanese brackets hxi γ :¼; wð ≥ , ≢ 0Þ and the initial data are continuous functions in R N . We determine the Fujita exponent for global and non-global solutions of the problem, depending strictly on N, γ and σ, which complete the ones for the nonnegative solutions in J. Math. Anal. Appl. 251 (2000) 624-648 for N ¼ 1, 2. It is so interesting that the inhomogeneous term leads to the discontinuity of this critical exponent with respect to σ at zero.

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