On the Fučik spectrum and a resonance problem for the image-Laplacian with a nonlinear boundary condition Original Research Article

In this paper we prove that there exists a first curve of the Fučik spectrum of the problem Δpu=|u|p-2uΔpu=|u|p-2u in ΩΩ with a nonlinear boundary condition given by |∇u|p-2∂u/∂ν=α(u+)p-1-β(u-)p-1|∇u|p-2∂u/∂ν=α(u+)p-1-β(u-)p-1 on the boundary of the domain. We also prove that there exists a sequence of curves of the Fučik spectrum which exist locally in the neighborhood of suitable eigenvalues of the p-Laplacian with a nonlinear boundary condition. Finally, we study a resonance problem with respect to the Fučik spectrum.