  We consider nonlocal equations of the type \[ (-\Delta_{p})^{s}u = \mu \quad
\text{in }\Omega, \] where $\Omega \subset \mathbb{R}^{n}$ is either a bounded
domain or the whole $\mathbb{R}^{n}$, $\mu$ is a Radon measure on $\Omega$,
$0<s<1$ and $1<p<n/s$. Especially, we extend the existence, regularity and
Wolff potential estimates for SOLA (Solutions Obtained as Limits of
Approximations), established by Kuusi, Mingione, and Sire (Comm. Math. Phys.
337:1317--1368, 2015), to the strongly singular case $1<p\le2-s/n$. Moreover,
using Wolff potentials and Orlicz capacities, we present both a sufficient and
a necessary conditions for the existence of SOLA to nonlocal equations of the
type \[ (-\Delta_{p})^{s}u = P(u) + \mu \quad \text{in }\Omega, \] where
$P(\cdot)$ is either a power function or an exponential function.
