Existence of Semiclassical Ground State Solutions for a Class of N-Laplace Choquard Equation with Critical Exponential Growth

In this paper, we discuss the following N-Laplace Choquard equation {-epsilon(N)Nv+V(x)|v|(N-2)v=epsilon mu-N(|x|-mu & lowast;F(v))f(v),x is an element of RN,u is an element of W1,N(RN), where N >= 2,mu is an element of(0,N),Delta Nv=div(|del v|N-2 del v) is the N-Laplace operator,epsilon is a positive parameter ,V is a differentiable potential,Fis the primitive off with critical exponential growth in the sense of Trudinger-Moser. To address the challenges stemming from the presence of an exponential growth given by fand the quasilinear nature of the equation, we conduct meticulous analyses. This enables us to establish an intricate threshold for the Mountain-Pass minimax level and demonstrate the presence and concentration of semiclassical ground state solutions for the equation in question.