An extension of Eliezer's theorem on the Abraham-Lorentz-Dirac equation

In 1943 Eliezer showed that, according to the Abraham-Lorentz-Dirac equation, a point charge cannot fall on a centre of attractive Coulombian forces, if one considers only motions constrained on a line. In other words, the Abraham-Lorentz-Dirac equation on a line does not admit solutions x(t) such that x → 0 for t → tc, with either a finite or infinite tc. In this paper it is shown that this remain true for the full three-dimensional problem.