Necessary and sufficient condition for the positivity of the Green function of a boundary value problem for a fourth-order equation on a graph (Q2352644)

A model of a structure of rigidly connected rods is studied. In particular, a fourth order differential equation is considered on a geometric graph, i.e. a connected set that has the structure of a network and is embedded in \(\mathbb{R}^{N}\). Necessary and sufficient conditions for the positivity of the Green function are investigated. These conditions are given in terms of the properties of a uniquely determined system of solutions of the equation on the graph allowing one to substantiate them economically using computer techniques.