  This paper is devoted to the study of the following autonomous Kirchhoff-type
equation $$-M\left(\int_{\mathbb{R}^N}|\nabla{u}|^2\right)\Delta{u}=
f(u),~~~~u\in H^1(\mathbb{R}^N),$$ where $M$ is a continuous non-degenerate
function and $N\geq2$. Under suitable additional conditions on $M$ and general
Berestycki-Lions type assumptions on the nonlinearity $f$, we establish several
existence results of multiple solutions by variational methods, which are also
naturally interpreted from a non-variational point of view.
