  We consider the following doubly nonlocal nonlinear logistic problem driven
by the fractional $p$-Laplacian
  \begin{equation*}
  \pl u = f(x,u) -\cq ~\text{in}~ \O,
  ~u=0 ~\text{in}~ \Rn\setminus\O.
  \end{equation*}
  Here $ \O \subset \Rn (N\geq2)$ is a bounded domain with $ C^{1,1}$ boundary
$\partial \O$, $ s \in (0,1) $, $p \in (1,\infty)$ are such that $ps < N$. Also
$p_{s,\a}^\#\leq r<\infty$
  , where $p_{s,\a}^\#=(2N-\a)/2N$.
  Under suitable and general assumptions on the nonlinearity $f$, we study the
existence, nonexistence, uniqueness, and regularity of weak solutions. As for
applications, we treat cases of subdiffusive type logistic Choquard problem. We
also consider in the superdiffusive case the Brezis-Nirenberg type problem with
logistic Choquard and show the existence of a nontrivial solution for a
suitable choice of $\l$. Finally for a particular choice of $f$ viz. $f(x,t)=\l
t^{q-1}$ with $1<p<2r<q$, we show the existence of at least one energy nodal
solution.
