LAUSR

In this paper, we study the Choquard equation involving the p$$ p $$ ‐Laplacian operator with a Lp$$ {L}^p $$ ‐norm constraint. We present Gagliardo‐Nirenberg inequality of Hartree type with best constant in the p$$ p $$ ‐Laplacian setting. For a Lp−$$ {L}^p- $$ supercritical perturbation μ|u|s−2u$$ \mu {\left|u\right|}^{s-2}u $$ with μ>0$$ \mu >0 $$ , under different assumptions on q$$ q $$ , we prove several existence results. In particular, we obtain the existence of ground states for the Hardy‐Littlewood‐Sobolev lower critical exponent case q=pα$$ q={p}_{\alpha } $$ . Finally, we prove existence and nonexistence of ground states for pα≤q