On the disconjugacy property of an equation on a graph

Resumo

Under study is the disconjugacy theory of forth order equations on a geometric graph. The definition of disconjugacy is given in terms of a special fundamental system of solutions to a homogeneous equation. We establish some connections between the disconjugacy property and the positivity of the Green’s functions for several classes of boundary value problems for forth order equation on a graph. We also state the maximum principle for a forth order equation on a graph and prove some properties of differential inequalities.