In this paper we deal with the following fractional Kirchhoff equation \begin{ equation*} \left(p+q(1-s) \iint_{ \mathbb{ R}^{ 2N}} \frac{ |u(x)- u(y)|^{ 2}}{ |x-y|^{ N+2s}} \, dx\,dy \right)(-\Delta)^{ s}u = g(u) \mbox{ in } \mathbb{ R}^{ N}, \end{ equation*} where $s\in (0,1)$, $N\geq 2$, $p>0$, $q$ is a small positive parameter and $g: \mathbb{ R}\rightarrow \mathbb{ R}$ is an odd function satisfying Berestycki-Lions type assumptions. By using minimax arguments, we establish a multiplicity result for the above equation, provided that $q$ is sufficiently small.
Categories: math.AP