Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 24 (2017), No. 4, 1197--1215Copyright Heldermann Verlag 2017 Existence of Solutions for a Nonlocal Variational Problem in R2 with Exponential Critical Growth Claudianor O. Alves Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática, CEP: 58429-900, Campina Grande - Pb, Brazil coalves@dme.ufcg.edu.br Minbo Yang Dept. of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China mbyang@zjnu.edu.cn [Abstract-pdf] We study the existence of nontrivial solutions 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 $s$. By assuming that the nonlinearity $f(x,s)$ has an exponential critical growth at infinity, we prove the existence of solutions by variational methods. Keywords: Nonlocal nonlinearities, exponential critical growth, ground state solution. MSC: 35J50, 35J60, 35A15 [ Fulltext-pdf  (145  KB)] for subscribers only.