Singularity and Decay Estimates for a Degenerate Parabolic Equation

In order to prove the existence and multiplicity of positive solutions, it is important to obtain a priori bounds for their positive solutions. It is well known that Liouville theorem would imply optimal universal estimates for solutions of related initial or initial boundary value problems, including estimates of their singularities and decay via the rescaling method (see [1, 2]). +e following Liouville result [3] will play an important role in our proof of singularity estimates.