On a class quasilinear Schrödinger equations in ℝⁿ

Abstract

We study the existence and multiplicity of solutions for quasilinear elliptic equations of the form

where , is the Laplacian. Our approach is variational and covers the case when the potential may vanish and be unbounded below and the nonlinear term admits general growth and can be unbounded in variable .

Keywords:

• variational methods
• critical points
• Laplacian
• vanishing potential
• nonlinear Schrödinger equations
• bounded states

AMS Subject Classifications:

• 35J20
• 35J60
• 35B33

Additional information

Funding

Research partially supported by the National Institute of Science and Technology of Mathematics INCT-Mat, CAPES and CNPq.