Nonnegative solutions for the fractional Laplacian involving a nonlinearity with zeros

We study the nonlocal nonlinear problem{(-Delta)(s)u = lambda f(u) in Omega,u = 0 on R-N\Omega, (P-lambda)where Omega is a bounded smooth domain in R-N, N > 2s, 0 < s < 1; f : R ->[0,infinity) is a nonlinear continuous function such that f(0) = f(1) = 0 a