Nonuniqueness for fractional parabolic equations with sublinear power-type nonlinearity

Abstract

We show that a parabolic equation with the fractional Laplacian and a sublinear power-type nonlinearity posed in a bounded time-space cylinder and coupled with zero initial condition and zero nonlocal Dirichlet condition, has at least one nontrivial nonnegative finite energy solution. This fact contrasts with the (super)linear case in which the only bounded finite energy solution is identically zero.