%0 Journal Article
%T Existence of solutions for a nonlocal variational problem in $\mathbb{R}^2$ with exponential critical growth
%A Claudianor O. Alves
%A Minbo Yang
%J Mathematics
%D 2015
%I arXiv
%X We study the existence of solution for the following class of nonlocal problem, $$ -\Delta u +V(x)u =\Big( I_\mu\ast F(x,u)\Big)f(x,u) \quad \mbox{in} \quad \mathbb{R}^2, $$ where $V$ is a positive periodic potential, $I_\mu=\frac{1}{|x|^\mu}$, $0<\mu<2$ and $F(x,s)$ is the primitive function of $f(x,s)$ in the variable $s$. In this paper, by assuming that the nonlinearity $f(x,s)$ has an exponential critical growth at infinity, we prove the existence of solutions by using variational methods.
%U http://arxiv.org/abs/1508.04488v1