Multiple solutions for nonlinear elliptic problems involving fractional operators

In this paper, we employ a variational method to establish the existence of multiple solutions to a nonlinear elliptic problem involving fractional operators. More precisely, by applying Ekeland’s variational principle to each of three constructed sets, we prove that the problem under consideration admits a solution within each of them. Furthermore, these solutions exhibit the following properties: One is positive, another is negative, and the third changes sign.