Generalized quasilinear Schrödinger equations with concave functions <inline-formula><tex-math id="M1">\begin{document}$ l(s^2) $\end{document}</tex-math></inline-formula>

We establish the existence of nontrivial solutions for the following quasilinear Schrödinger equation with subcritical or critical growth: \begin{document} $ \begin{equation*}-Δ u+W(x)u^{2α-1}-ul'(u^2)Δ l(u^2) = f(u) \ \mbox{or}\ h(u)+u^{2^*-1},\ x∈\mathbb{R}^N,\end{equation*} $ \end{document} where $W(x):\mathbb{R}^N \to \mathbb{R} $ is a given potential and $ l,h,f $ are real functions, $ u>0,$ $ 2^* = 2N/(N-2), $ $ N≥3 $. Our results cover physical models $ l(s) = s^{\frac{α}{2}}, $ $ \frac{1}{2}<α<1. $