Abstract: The paper is devoted to the problems of disconjugacy of fourth-order differential equations on a graph. We introduce the concept of critical disconjugacy. Critical disconjugacy allows us to generalize the notion of exact interval of disconjugacy in the classical theory. We give the definition of disconjugacy in terms of the properties of a special fundamental system of solutions of an equation on a graph. This definition introduces new features into the theory, but it preserves the basic properties of the one-dimensional theory.

Keywords: differential equation on a graph, disconjugacy, boundary value problem, Green's function

For citation: Kulaev R. Ch. On the disconjugacy of a differential equation on a graph // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 31-40. DOI 10.23671/VNC.2017.3.7110

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