Concentrating normalized solutions for 2D nonlocal Schrodinger equations with critical exponential growth

We study the existence of solutions to nonlocal Schr"odinger problems with different types of potentials $$\displaylines{ -\Delta u +W(x) u=\sigma u +\kappa[|x|^{-\mu}\ast F(u)]f(u)\quad \text{in }\mathbb{R}^2, \cr \int_{\mathbb{R}^2}|u|^2dx=a^2, }$$ where \(a\neq0\), \(\sigma\in\mathbb{R}\) is known as the Lagrange multiplier, \(\kappa>0\) is a parameter, \(W\in \mathcal{C}(\mathbb{R}^2)\) is the nonnegative external potential, \(\mu\in(0,2)\), and \(F\) denotes the primitive function of \(f\in \mathcal{C}(\mathbb{R})\) which has critical exponential growth in the Trudinger-Moser sense at infinity. We prove that the problems admit at least a positive solution, and we analyze the concentrating behavior. For more information see https://ejde.math.txstate.edu/Volumes/2025/34/abstr.html