Critical Exponents For Slow Diffusion Equations With A Potential

In this paper, we study the critical exponent pc of the nonnegative solutions to the Cauchy problem for a slow diffusion equation. We obtain the following results:Every nontrivial solution blows up in finite time when m≤p≤pc, V(x)≤ω/|x|2, and there are both global and non-global solutions if p>pc, when V(x)≥ω/|x|2.