Multiple solutions to some singular nonlinear Schrodinger equations

Abstract

We consider the equation $$ - h^2 Delta u + V_varepsilon(x) u = |u|^{p-2} u $$ which arises in the study of standing waves of a nonlinear Schrodinger equation. We allow the potential $V_varepsilon$ to be unbounded below and prove existence and multiplicity results for positive solutions.

Keywords

• nonlinear Schrodinger equations
• singular potentials
• variational methods
• Ljusternik--Schnirelman category.