A multiplicity result for a fractional Kirchhoff equation in $mathbb{R}^{N}$ with a general nonlinearity

In this paper, we deal with the following fractional Kirchhoff equation egin{equation*} left( p +q(1-s) iint_{mathbb{R}^{2N}} rac{|u(x) - u(y)|^{2}}{|x-y|^{N+2s}} dxdy ight) (-Delta)^{s}u = g(u) &mbox{ in } mathbb{R}^{N}, end{equation*} where $sin (0, 1)$, $Ngeq 2$, $p>0$, $q$ is a small positive parameter and $g:mathbb{R} ightarrow mathbb{R}$ 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.