On the disconjugacy of a differential equation on a graph. (Russian. English summary) Zbl 1453.34037

Kulaev, Ruslan Chermenovich

Vladikavkaz. Mat. Zh. 19, No. 3, 31-40 (2017).

Summary: 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.

MSC:

34B45	Boundary value problems on graphs and networks for ordinary differential equations
34B27	Green’s functions for ordinary differential equations
34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

differential equation on graph; disconjugacy; boundary value problem; Green’s function

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