Sign-changing solutions of the nonlinear heat equation with persistent singularities

Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1

We study the existence of sign-changing solutions to the nonlinear heat equation ${\partial }_{t}u=\Delta u+|u{|}^{\alpha }u$ on ${\mathbb{R}}^N$, $N\ge 3$, with $\frac{2}{N-2}<\alpha <{\alpha }_0$, where…