Existence and nonexistence of least energy nodal solution for a class of elliptic problem in ${\mathbb{R}}^2$

Abstract

In this work, we prove the existence of least energy nodal solution for a class of elliptic problem in both cases, bounded and unbounded domain, when the nonlinearity has exponential critical growth in ${\mathbb{R}}^2$. Moreover, we also prove a nonexistence result of least energy nodal solution for the autonomous case in whole ${\mathbb{R}}^2$.