The Fučík Spectra for Multi-point Boundary-value Problems

We study the structure of the Fuč́ık spectra for the linear multipoint differential operators. We introduce a variational approach in order to obtain a robust and global algorithm which is suitable for the exploration of unknown Fuč́ık spectrum structure. We apply our approach in the case of the four-point selfadjoint differential operator of the fourth order which is closely connected to the nonlinear model of a suspension bridge with two towers. Moreover, we reconstruct the Fuč́ık spectra in the case of four-point non-selfadjoint ordinary differential operators of the second order in order to demonstrate their non-trivial and interesting structure.