On a class of fractional Schrödinger equations in with sign-changing potential

Abstract

We are interested in finding solutions to a class of problems involving the fractional Laplacian operator. Specifically, we study the equation

where , denotes the fractional Laplacian of order s, , V(x) is a continuous and unbounded potential which may change sign, and the nonlinearity is a continuous function which may be unbounded in x since its growth is controlled by V(x) and has subcritical growth in in the sense of the Sobolev embedding. Assuming suitable conditions under V(x) and and applying a approach variational, we prove the existence of the multiplicity of solution for this equation.

Keywords:

• Variational methods
• critical points
• fractional Laplacian

AMS Subject Classifications:

• 35J20
• 35J60
• 35R11

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research partially supported by CNPq [grant number 308758/2013-7].