I will present our recent result on an eigenvalue problem involving the (p,q)-fractional Laplace operators, under  the corresponding  nonlocal (p,q)-Neumann boundary condition.  On an  open bounded set with smooth boundary,  we  describe the spectrum of the problem considered, which complements some results from local to nonlocal comprehensive analysis. Due to the nonlocal feature of the operators appearing in the equations, some purely nonlocal situations occur (crossing) and bring a significant difference in the study of nonlocal problems compared to local ones.

This is a joint work with E. Zongo.