Let $s\in(0,1),$ $1<p<\frac{ N}{ s}$ and $\Omega\subset\mathbb{ R}^N$ be an open bounded set. In this work we study the existence of solutions to problems ($E_\pm$) $Lu\pm g(u)=\mu$ and $u=0$ a.e. in $\mathbb{ R}^N\setminus\Omega,$ where $g\in C(\mathbb{ R})$ is a nondecreasing function, $\mu$ is a bounded Radon measure on $\Omega$ and $L$ is an integro-differential operator with order of differentiability $s\in(0,1)$ and summability $p\in(1,\frac{ N}{ s}).$ More precisely, $L$ is a fractional $p-$Laplace type operator. We establish sufficient conditions for the solvability of problems ($E_\pm$). In the particular case $g(t)=|t|^{ \kappa-1}t;$ $\kappa>p-1,$ these conditions are expressed in terms of Bessel capacities.
Categories: math.AP