The Choquard logarithmic equation involving a nonlinearity with exponential growth

Abstract

In the present work we are concerned with the Choquard Logarithmic equation $-\Delta u+au+\lambda (\ln |\cdot |\ast |u{|}^2)u=f(u)$ in ${\mathbb{R}}^2$, for $a>0$, $\lambda >0$ and a nonlinearity $f$ with exponential critical growth. We prove the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution. Also, we provide these results under a symmetric setting, taking into account subgroups of $O(2)$.