Sign-changing solutions for some nonhomogeneous nonlocal critical elliptic problems.

We construct multiple sign-changing solutions for the nonhomogeneous nonlocal equation (-Δ_Ω)^su = |u|4/N-2s u + ε ƒ(x) in Ω, under zero Dirichlet boundary conditions in a bounded domain Ω in R^N, N > 4s, s ∈ (0,1], with f ∈ L∞(Ω), ƒ ≥ 0 and ƒ ≠ 0. Here, ε > 0 is a small parameter, and (−∆Ω)^s represents a type of nonlocal operator sometimes called the spectral fractional Laplacian. We show that the number of sign-changing solutions goes to infinity as ε → 0 when it is assumed that Ω and ƒ have certain smoothness and possess certain symmetries, and we are also able to establish accurately the contribution of the nonhomogeneous term in the found solutions. Our proof relies on the Lyapunov-Schmidt reduction method. [ABSTRACT FROM AUTHOR]