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

In 1943 Eliezer showed that, according to the Abraham-Lorentz-Dirac equatio n, 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 Ab raham-Lorentz-Dirac equation on a line does not admit solutions x(t) such t hat x --> 0 for t --> t(c), with either a finite or infinite t, In this pap er it is shown that this remain true for the full three-dimensional problem .