Título: On coupled systems of nonlinear equations on $latex \mathbb{R}^{2}$ with critical exponential growth
Data: 17/02/2017 às 14:00 h
Local: Auditório da Unidade Acadêmica de Matemática
Resumo: In this talk we study the existence of positive ground state solutions to the following class of coupled systems
$latex
\left\{
\begin{array}{lr}
-\Delta u+u=f_{1}(u)+\lambda(x)v, & \mathbb{R}^{2},\\
-\Delta v+v=f_{2}(v)+\lambda(x)u, & \mathbb{R}^{2},
\end{array}
\right.
$
where the nonlinearities $latex f_{1}(s)$ and $latex f_{2}(s)$ have critical exponential growth motivated by a class of Trudinger-Moser inequality introduced by D.M. Cao (1992). Our approach is variational and based on minimization technique over the Nehari manifold. This is a joint work with J.M. do Ó.