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 $\exp ({\alpha }_0{s}^2)$ as $|s|\to \infty$, for some ${\alpha }_0>0$. In order to obtain our existence result we used minimax techniques combined with the Trudinger-Moser inequality.

Cited by in corpus (2)

• $n$Kirchhoff type equations with exponential nonlinearities
• Polyharmonic Kirchhoff type equations with singular exponential nonlinearities