Kirchhoff–Schrödinger equations in ℝ2 with critical exponential growth and indefinite potential

Abstract

We prove the existence of ground state solution for the nonlocal problem [Formula: see text] where [Formula: see text] is a Kirchhoff type function, [Formula: see text] may be negative and noncoercive, [Formula: see text] is locally bounded and the function [Formula: see text] has critical exponential growth. We also obtain new results for the classical Schrödinger equation, namely the local case [Formula: see text]. In the proofs, we apply Variational Methods besides a new Trudinger–Moser type inequality.