  In this contribution, we study a class of doubly nonlinear elliptic equations
with bounded, merely integrable right-hand side on the whole space
$\mathbb{R}^N$. The equation is driven by the fractional Laplacian
$(-\Delta)^{\frac{s}{2}}$ for $s\in (0,1]$ and a strongly continuous nonlinear
perturbation of first order. It is well known that weak solutions are in
genreral not unique in this setting. We are able to prove an $L^1$-contraction
and comparison principle and to show existence and uniqueness of entropy
solutions.
