Ground state solutions for Kirchhoff-type equations with a general nonlinearity in the critical growth

In this paper, we concern ourselves with the following Kirchhoff-type equations:\left\{\begin{aligned} \displaystyle-\biggl{(}a+b\int_{\mathbb{R}^{3}}\lvert% \nabla u\rvert^{2}\,dx\biggr{)}\triangle u+Vu&\displaystyle=f(u)\quad\text{in % }\mathbb{R}^{3},\\ \displaystyle u&\displaystyle\in H^{1}(\mathbb{R}^{3}),\end{aligned}\right.where a, b and V are positive constants and f has critical growth. We use variational methods to prove the existence of ground state solutions. In particular, we do not use the classical Ambrosetti–Rabinowitz condition. Some recent results are extended.