Absence of global periodic solutions for a Schrödinger-type nonlinear evolution equation

The problem of the absence of global periodic solutions for a Schrödinger-type nonlinear evolution equation with a linear damping term is investigated. It is proved that when the damping coefficient is nonnegative, the problem does not have global periodic solutions for any initial data, while when it is negative, the same is valid for “sufficiently large values” of the initial data.