Multiple solutions for quasilinear Schrödinger equations with a parameter

In this paper, we study the following quasilinear Schrödinger equations of the form−Δu+V(x)u−Δ(|u|2α)|u|2α−2u=g(x,u),x∈RN, where 1⩾α>12, V∈C(RN,R)V∈C(RN,R), g∈C(RN×R,R)g∈C(RN×R,R). Using some special techniques, the existence of positive solutions, negative solutions and sequence of high energy solutions are studied.