Abstract
In this paper, we investigate the magnetic nonlinear Kirchhoff equation [Formula: see text] where [Formula: see text] is a Kirchhoff-type function, [Formula: see text] and [Formula: see text] denote a magnetic potential and an electric potential, respectively, and [Formula: see text] has exponential critical growth. By combining variational methods with a monotonicity trick, we prove the existence of a ground state solution. In addition, our result does not require the nonlinearity [Formula: see text] to satisfy the Ambrosetti–Rabinowitz condition, which allows us to consider a broader class of nonlinearities. In this sense, our result extends and complements the results in Furtado and Zanata [Commun. Contemp. Math. 23 (2021), 2050030] and Wen et al. [Discrete Contin. Dyn. Syst. 42 (2022), 5783–5815].