On the existence and multiplicity of solutions for the $N$-Choquard logarithmic equation with exponential critical growth

In the present work we briefly explain how to adapt techniques already used in fractional and $p$-fractional Laplacian cases to obtain the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution, for the critical case, and the existence of infinitely many solutions, for the subcritical case, to the Choquard Logarithmic equation, $-\Delta_N u + a(x)|u|^{N-2}u + \lambda (\ln|\cdot|\ast |u|^{N})|u|^{N-2}u = f(u) $\text{ in }$ $\mathbb{R}$^N $,where$ a:$\mathbb{R}$^N \rightarrow $\mathbb{R}$ $,$ \lambda >0 $,$ N \geq 3 $and$f: $\mathbb{R}$ \rightarrow [0, \infty) $iscontinuousfunctionthatbehaveslike$ \exp(\alpha |u|^{\frac{N}{N-1}}) $atinfinity,for$ \alpha >0 $.