We investigate a class of generalized quasilinear Schrödinger equations
$ -{\rm div}(g^{2}(u)\nabla u)+g(u)g'(u)|\nabla u|^{2}+V(x)u=f(x,u) \mbox{ in }\mathbb{R}^{N},$
where $ g(u):\mathbb{R}\to\mathbb{R}^{+} $ is a nondecreasing function with respect to $ |u| $, the potential $ V(x) $ and the primitive of the nonlinearity $ f(x,u) $ are allowed to be sign-changing. Under some suitable assumptions, we obtain the existence of infinitely many nontrivial solutions. The proof is based on a change of variable as well as symmetric Mountain Pass Theorem.
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