In this paper we obtain a good geometric understanding of the Fučík spectrum of several fourth-order problems. This problem was raised by S. Fučík in , where it is asked to give a description of this set. The situation resembles the known cases of second-order equations, where analytic branches bifurcate from the eigenvalues in the diagonal.
"On the resonance set in a fourth-order equation with jumping nonlinearity." Differential Integral Equations 14 (3) 257 - 272, 2001. https://doi.org/10.57262/die/1356123327