Subcritical nonlocal problems with mixed boundary conditions

By using linking and del-theorems in this paper we prove the existence of multiple solutions for the following nonlocal problem with mixed Dirichlet-Neumann boundary data, {(-Delta)(s) u = lambda u + f(x, u) in Omega u = 0 on Sigma(D), partial derivative u/partial derivative v = 0 on Sigma(N,) where (-Delta)(s), s is an element of (1/2, 1), is the spectral fractional Laplacian operator, Omega subset of R-N, N > 2s, is a smooth bounded domain, lambda > 0 is a real parameter, nu is the outward normal to partial derivative Omega, Sigma(D), Sigma(N) are smooth (N - 1)-dimensional submanifolds of partial derivative Omega such that Sigma(D) boolean OR Sigma(N) = partial derivative Omega, Sigma(D) boolean AND Sigma(N) = : empty set Sigma(D) boolean AND (Sigma) over bar (N) = G is a smooth (N - 2)-dimensional submanifold of partial derivative Omega.