We first prove existence and uniqueness of non-negative solutions of the equation
in in the range 1 < p < 1 + 2/N, when initial data u(x, 0) = a|x|−2(p−1), x ≠ 0, for a > 0. It is proved that the maximal and minimal solutions are self-similar with the form
where g = ga satisfies
After uniqueness is proved, the asymptotic behaviour of solutions of
is studied. In particular, we show that
The case for a = 0 is also considered and a sharp decay rate of the above equation is derived. In the final, we reveal existence of solutions of the first and third equations above, which change sign.