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.