Comparison theorems for Green function of a fourth order boundary value problem on a graph

Abstract

In the work we develop the non-oscillation theory for fourth order equations on a geometric graph arising in modelling of rod junctions. The non-oscillation of an equation is defined in terms of the properties of a special fundamental system of solutions to the homogeneous equation. We describe the relation between non-oscillation property and the positivity of Green function to some classes of boundary value problems for fourth order equation on a graph.