2007 Conference on Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems. Electron. J. Diff. Eqns., Conference 18 (2010), pp. 33-44.

The Fucik spectra for multi-point boundary-value problems

Gabriela Holubova, Petr Necesal

Abstract:
We study the structure of the Fucik spectra for the linear multi-point differential operators. We introduce a variational approach in order to obtain a robust and global algorithm which is suitable for the exploration of unknown Fucik 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 Fucik 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.

Published July 10, 2010.
Math Subject Classifications: 34B10, 34B15, 34L05.
Key Words: Fucik spectrum; asymmetric nonlinearities; multi-point boundary value problem; suspension bridge with two towers.

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Gabriela Holubova
University of West Bohemia, Univerzitni 22
306 14 Plzen, Czech Republic
email: gabriela@kma.zcu.cz
Petr Necesal
University of West Bohemia, Univerzitni 22
306 14 Plzen, Czech Republic
email: pnecesal@kma.zcu.cz

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