Yor [@stroock_yor] and J.F. Le Gall [@LeGall_1983], [@LeGall_1984]. H.J. Engelbert and W. Schmidt [@engelbert_schmidt:1985], [@engelbert_schmidt:1989_III] derived rather weak necessary and sufficient conditions on existence and uniqueness of solutions to SDEs with generalized drift. More recently, R.F. Bass and Z.-Q. Chen [@bass_chen] also considered SDEs of type (\[eqn:SDE\_mvd\]).\
To treat the general equation (\[eqn:SDE\_mvd\]), in case of considering the right (resp., left, symmetric) local time the additional assumption $$\label{eqn:cond_atoms}
    \nu(\{x\}) < \frac{1}{2} \quad (\text{resp., } \nu(\{x\}) > -\frac{1}{2}, \ |\nu(\{x\})| < 1), \qquad x \in \mathbb{R}\,,$$ is posed on $\nu$ (cf. [@engelbert_schmidt:1985],[@engelbert_schmidt:1989_III],[@LeGall_1984],[@stroock_yor]). This condition allows to reduce Eq. (\[eqn:SDE\_mvd\]) to an equation without drift, i.e., an equation of type (\[eqn:SDE\_mvd\]) where the drift measure is the zero measure. Therefore, well-known conditions on existence and uniqueness of solutions to equations without drift can be used to derive conditions on existence and uniqueness of solutions to Eq. (\[eqn:SDE\_mvd\]) (see e.g. [@engelbert_schmidt:1985],[@engelbert_schmidt:1989_III]). More precisely, under condition (\[eqn:cond\_atoms\]) the integral equation $$\label{eqn:integral_eqn}
    g(x) = \left\{
                    \begin{array}{ll}
                        \displaystyle 1 - 2 \int_{[0,x]} F(g,y) \, \nu({\mbox{\upshape d}}y), & x \geq 0, \medskip \\
                        \displaystyle 1 + 2 \int_{(x,0)} F(g,y) \, \nu({\mbox{\upshape d}}y), & x \geq 0,
                    \end{array}
                 \right.$$ where $$F(g,x) = g(x-) \quad(\text{resp., } g(x), \ \left(g(x) 