A global characterization of the Fucik spectrum for a system of ordinary differential equations

The Fucik spectrum for systems of second order ordinary differential equations with Dirichlet or Neumann boundary values is considered: it is proved that the Fucik spectrum consists of global C1 surfaces, and that through each eigenvalue of the linear system pass exactly two of these surfaces. Further qualitative, asymptotic and symmetry properties of these spectral surfaces are given. Finally, related problems with nonlinearities which cross asymptotically some eigenvalues, as well as linear- superlinear systems are studied.