Ground state solutions for a nonlocal equation in ${\mathbb{R}}^2$ involving vanishing potentials and exponential critical growth

Francisco S. B. Albuquerque, Marcelo C. Ferreira, Uberlândio B. Severo

In this paper, we study the following class of nonlinear equations: $$-\Delta u+V(x)u=\left[|x{|}^{-\mu }\ast (Q(x)F(u))\right]Q(x)f(u),x\in {\mathbb{R}}^2,$$ where $V$ and $Q$ are contin…