The Choquard logarithmic equation involving a nonlinearity with exponential growth
DOI:
https://doi.org/10.12775/TMNA.2021.062Keywords
Choquard logarithmic equations, exponential growth, variational techniques, ground state solutionAbstract
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) $.References
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