On critical exponents for some quasilinear parabolic equations

We study the Cauchy problem for the quasilinear parabolic equation where p > 1 is a parameter and ψ is a smooth, bounded function on (1, ∞) with ? ? sψ′(s)/ψ(s) ? θ for some θ > 0. If 1 < p < 1 + 2/N, there are no global positive solutions, whereas if p > 1 + 2/N, there are global, positive solutions for small initial data.