Discrete Fučík spectrum - anchoring rather than pasting
Department of Mathematics, University of West Bohemia, Univerzitni 22, Pilsen, 30614, Czech Republic
Boundary Value Problems 2013, 2013:67 doi:10.1186/1687-2770-2013-67Published: 29 March 2013
In this short note we study a simple discrete Fučík spectrum. Trying to imitate standard continuous pasting procedures, we derive a more complicated discrete analogue - anchoring. Using this technique, we show that the problem of finding the parametrization of the second discrete Fučík branch is equivalent to solving a transcendent equation . Based on this equivalence, we state a conjecture that already the second branch has no elementary parametrization, i.e., it cannot be described by a finite number of elementary functions.
MSC: 39A12, 34B15.