Ground state solution for a Kirchhoff problem with exponential critical growth

We establish the existence of a positive ground state solution for a Kirchhoff problem in $\mathbb{R}^2$ involving critical exponential growth, that is, the nonlinearity behaves like $\exp(α_{0}s^{2})$ as $|s| \to \infty$, for some $α_{0}>0$. In order to obtain our existence result we used minimax techniques combined with the Trudinger-Moser inequality.

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