Wolff potentials and nonlocal equations of Lane-Emden type

We consider nonlocal equations of the type \ (-₏) ^su = in, \ where R^n is either a bounded domain or the whole R^n, is a Radon measure on, 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<p2-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 \ (-₏) ^su = P (u) + in, \ where P () is either a power function or an exponential function.