Monotonicity of eigenvalues of the fractional p-Laplacian with singular weights.

We study a nonlinear, nonlocal eigenvalue problem driven by the fractional p-Laplacian with an indefinite, singular weight chosen in an optimal class. We prove the existence of an unbounded sequence of variational eigenvalues and variational characterizations of the first and second eigenvalues. Then, by means of such characterizations, we prove strict decreasing monotonicity of such eigenvalues with respect to the weight function.