Equations with Vanishing PotentialsР WANG Yanan, TENG KaiminР (School of Mathematics, Taiyuan University of Technology, Jinzhong 030600,China )Р Abstract: This paper is devoted to studying the quasilinear Schr¨odinger equations of p-LaplaceР type with vanishing potentials, and the existence of positive solutions is established via mountain passР theorem and Moser iteration.Р Key words: Quasilinear Schr¨odinger equation; p-Laplace; Vanishing potential