Self-similar solutions for the heat equation with a positive non-Lipschitz continuous, semilinear source term

We prove the existence of at least three selfsimilar solutions (among which two are changing sign solutions) for a semilinear heat equation with a non-lipschitz, non-linear source term when the equation is complemented with a suitable initial datum which is always negative except in a single point where it is zero. In this way we prove a non-uniqueness result, which is in contrast with some uniqueness results previously proved (when different kinds of initial data are assigned)