Fractional eigenvalues

We study the non-local eigenvalue problem 2 integral(Rn) vertical bar u(y) - u(x)|p(-2)(u(y) - u(x))/|y - x|(alpha p) dy + lambda|u(x)|p(-2)u(x)=0 for large values of p and derive the limit equation as p -> infinity. Its viscosity solutions have many interesting properties and the eigenvalues exhibit a strange behaviour.