Existence and multiplicity of solutions for a class of generalized quasilinear Schrödinger equations

This paper focuses on the following generalized quasilinear Schrödinger equations−div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=f(x,u),x∈RN, where N≥3, g(s):R→R+ is a nondecreasing function with respect to |s|. By using a change of variables and variational methods, we obtain the existence and multiplicity of nontrivial solutions for the above problem when the nonlinearity is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition.