Multiple solutions for a Kirchhoff-type equation with general nonlinearity

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