Existence of a mountain pass solution for a nonlocal fractional $(p, q)$-Laplacian problem

Here, a nonlocal nonlinear operator known as the fractional $(p,q)$ ( p , q ) -Laplacian is considered. The existence of a mountain pass solution is proved via critical point theory and variational methods. To this aim, the well-known theorem on the construction of the critical set of functionals with a weak compactness condition is applied.