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

Abstract

Abstract 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.

Keywords

• Fractional Laplacian equations
• Variational methods
• Fractional eigenvalue problems
• Mountain pass theorem