Non-Nehari manifold method for a class of generalized quasilinear Schrödinger equations

In this paper, we study the following generalized quasilinear Schrödinger equation −div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=f(x,u),x∈RN,where N≥3, 2∗=2NN−2, g∈C1(R,R+), V(x) and f(x,u) are 1-periodic on x. By using a change of variable, we obtain the existence of ground states solutions. Unlike the Nahari manifold method, the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the manifold by using the diagonal method.