The Choquard logarithmic equation involving a nonlinearity with exponential growth - Böer, Eduardo de S.; Miyagaki, Olímpio H. (Topological Methods in Nonlinear Analysis, 2022)
In the present work, we are concerned with the Choquard Logarithmic equation$-Δ u + au + λ (\ln|·|* |u|^{2})u = f(u)$ in $ \mathbb{R}^2$, for $ a> 0 $, $ λ > 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) $.