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We consider a $p$-fractional Choquard-type equation \[ (-\Delta)_p^su+a|u|^{p-2}u=b(K\ast F(u))F'(u)+\varepsilon_g |u|^{p_g-2}u \quad\text{in$\mathbb{R}^N$}, \] where $0<s<1<p<p_g\leq p_s^*$, $N \geq \max\{2ps+\alpha,p^2s\}$, $a,b,\varepsilon_g\in (0,\infty)$, $K(x)= |x|^{-(N-\alpha)}$, $\alpha\in(0,N)$, and $F$ is a doubly critical nonlinearity in the sense of theHardy-Littlewood-Sobolev inequality. It is noteworthy that the localnonlinearity may also have critical growth. Combining Brezis-Nirenberg's methodwith some new ideas, we obtain the ground state solutions via the mountain passlemma and a generalized Lions-type theorem.

Ground states for $p$-fractional Choquard-type equations with critical local nonlinearity and doubly critical nonlocality