In this article, we study the quasilinear Schrödinger equation
$$ -\triangle (u)+V(x)u-\triangle \bigl(u^{2}\bigr)u=g(x,u), \quad x\in \mathbb{R}^{N}, $$
where the potential
$V(x)$
and the primitive of
$g(x,u)$
are allowed to be sign-changing. Under more general superlinear conditions on g, we obtain the existence of infinitely many nontrivial solutions by using the mountain pass theorem. Recent results in the literature are significantly improved.
