A nonlocal coupled system involving N-Laplacian operator: existence and asymptotic behavior of positive solutions

In this paper, we study the existence of positive solutions for a nonlocal singular elliptic coupled system involving N-Laplace operator. The source term of the system is expressed as the sum of two components: one with subcritical, critical, or supercritical exponential growth controlled by the Trudinger–Moser inequality, and the other being singular at the origin. We also investigate the asymptotic behavior of the solutions with respect to the parameters. Furthermore, we prove that no solutions exist for our system in dimension $N=2$ .