Multiple Solutions for a Quasilinear Schrödinger Equation on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}^{N}$\end{document}

The multiplicity of positive weak solutions is established for quasilinear Schrödinger equations −Lpu+(λA(x)+1)|u|p−2u=h(u) in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}^{N}$\end{document}, where Lpu=ϵpΔpu+ϵpΔp(u2)u, A is a nonnegative continuous function and nonlinear term h has a subcritical growth. We achieved our results by using minimax methods and Lusternik-Schnirelman theory of critical points.