The qualitative theory of fourth-order differential equations on a graph (Q2113583)

This work develops a theory of disconjugacy for fourth-order equations on metric graphs. Such equations model deformation systems of beams connected by elastic pin-joints. The theory allows to obtain results analogous to those obtained in the theory of second order equations. The notion of disconjugacy is defined in several natural ways which are shown to be equivalent. In particular it is proved that an equation is disconjugate if and only if the Green function corresponding to a related boundary value problem is everywhere positive.