SEQUENCES OF WEAK SOLUTIONS FOR FRACTIONAL EQUATIONS

This work is devoted to study the existence of infinitely many weak solutions to nonocal equations involving a general integrodifferential operator of fractional type. These equations have a variational structure and we find a sequence of nontrivial weak solutions for them exploiting the Z(2)-symmetric version of the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. As a particular case, we derive an existence theorem for the fractional Laplacian, finding nontrivial solutions of the equation {(-Delta)(s)u = f(x, u) in Omega, u = 0 in R-n\Omega. As far as we know, all these results are new and represent a fractional version of classical theorems obtained working with Laplacian equations.