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In this paper, critical point theory is used to show the existence of nontrivial solutions for a class of generalized quasilinear Schrödinger equations $ \begin{equation*} -\Delta_pu-{|u|}^{\sigma-2}uh'({|u|}^\sigma)\Delta_ph({|u|}^\sigma) = f(x,u) \end{equation*} $ in a smooth bounded domain $ \Omega\subset{\mathbb{R}}^N $ with Dirichlet boundary conditions. Our result covers some typical physical models.