In this article we present the existence of infinitely many non-radial positive or sign-changing solutions for the following FitzHugh–Nagumosystem:
$$\begin{aligned} \left\{ \begin{array}{ll} \Delta u-a(|x|)u+g(u)-\delta v=0, \quad & x\in \mathbb {R}^N,\\ \Delta v+u=0, & x\in \mathbb {R}^N,\\ u(x), ~v(x)\rightarrow 0, & \text{ as }~ |x|\rightarrow +\infty ,\\ \end{array}\right. \end{aligned}$$
where
$$N\ge 5$$
,
$$\delta >0$$
,
$$g(u)=(a_0+1)u^2-u^3$$
,
$$0
