Ground State Solution for a Kirchhoff Problem with Exponential Critical Growth

Abstract

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 $${exp(\alpha_0s^2)}$$ as $${|s| \rightarrow \infty}$$ , for some $${\alpha_0 > 0}$$ . In order to obtain our existence result we used minimax techniques combined with the Trudinger-Moser inequality.