On a semilinear parabolic equation with inverse-square potential (Q619698)

The authors study existence and uniqueness, nonexistence and nonuniqueness of nonnegative solutions to a semilinear parabolic equation with inverse-square potential. Analogous existence and nonexistence results for the companion elliptic equation were proved by Brezis, Dupaigne and Tesei. Punzo and Tesei use semigroup estimates to reach this result. Concerning nonuniqueness, the authors extend, ina non trivial way, the results proved by Ni and Sacks for the case without potential.