Critical quasilinear Schrodinger equation with sign-changing potential

Abstract

We study the existence of nontrivial solutions for a class of quasilinear Schrodinger equations in R^N with critical nonlinearity, where the potential is allowed to change signs. The quasilinear equations are reduced to semilinear equations by using a change of variable. The geometric hypotheses of a mountain pass theorem without compactness conditions are satisfied so that the equation possesses a nontrivial solution.

Keywords

• Quasilinear Schrodinger equation
• critical growth
• sign-changing potential
• mountain pass theorem
• (PS)c sequence