
Journal of Convex Analysis 24 (2017), No. 4, 11971215 Copyright Heldermann Verlag 2017 Existence of Solutions for a Nonlocal Variational Problem in R^{2} with Exponential Critical Growth Claudianor O. Alves Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática, CEP: 58429900, 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 [Abstractpdf] 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 [ Fulltextpdf (145 KB)] for subscribers only. 