  In the paper \cite{carati95} it was shown that, for motions on a line under
the action of a potential barrier, the third-order Abraham-Lorentz-Dirac
equation presents the phenomenon of nonuniqueness of nonrunaway solutions.
Namely, at least for a sufficiently steep barrier, the physical solutions of
the equation are not determined by the "mechanical state" of position and
velocity, and knowledge of the initial acceleration too is required. Due to
recent experiments, both in course and planned, on the interactions between
strong laser pulses and ultra relativistic electrons, it becomes interesting to
establish whether such a nonuniqueness phenomenon extends to the latter case,
and for which ranges of the parameters. In the present work we will consider
just the simplest model, i.e., the case of an electromagnetic plane wave, and
moreover for the Abraham-Lorentz-Dirac equation dealt with in the
nonrelativistic approximation. The result we found is that the nonuniqueness
phenomenon occurs if, at a given frequency of the incoming wave, the field
intensity is sufficiently large. An analytic estimate of such a threshold is
also given. At the moment it is unclear whether such a phenomenon applies also
in the full relativistic case, which is the one of physical interest.
