In this paper, we deal with a class of non-autonomous Kirchhoff equations, namely, \(-(a + b\int _{\mathbb {R}^N}|\nabla u|^2\,\text {d}x)\Delta u - \mu u = K(x)|u|^{p-2}u\) in \(\mathbb {R}^N\) , where \(1 \le N \le 4\) , \(a, b>0\) are constants, \(\mu \in \mathbb {R}\) is unknown and appears as a Lagrange multiplier, \(2<p<2^*\) and \(K \in C(\mathbb {R}^N, \mathbb {R})\) is a bounded potential function satisfying \(\inf _{\mathbb {R}^N} K >0\) . Under certain additional assumptions on the potential K, the sharp existence of normalized ground state solutions is obtained by investigating equivalently the associated \(L^2\) -constrained minimization problem. Our main results extend and improve the corresponding results in the previous papers.
