Multiple solutions for a class of quasilinear Schrödinger equations in ℝ N

In this work, we study the existence of multiple solutions to a class of quasilinear Schrödinger equation −Δpu+V(x)up−2u−Δp(u2α)u2α−2u=g(u),x∈RN, where Δpu=div(∇up−2∇u) is the p − Laplacian operator and p ∈ [2α, N], α>12 is a parameter. The potential V ∈ C(ℝN) is positive and bounded in ℝN. g(u) is odd and continuous. Using symmetric mountain pass lemma, we obtain infinitely many solutions to Schrödinger equation.