Disconjugacy of fourth-order equations on graphs

被引：7

作者：

Kulaev, R. Ch. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Southern Math Inst, Vladikavkaz Sci Ctr, Vladikavkaz, Russia

[2] North Ossetia State Univ, Vladikavkaz, Russia

来源：

SBORNIK MATHEMATICS | 2015年 / 206卷 / 12期

关键词：

disconjugacy; differential equation on a graph; Green's function; maximum principle; conjugacy; ORDER;

D O I：

10.1070/SM2015v206n12ABEH004512

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper develops the theory of disconjugacy of fourth-order equations on geometric graphs which arises in modelling rod structures. The disconjugacy of an equation is defined in terms of a special fundamental system of solutions of the homogeneous equation. The disconjugacy property is shown to be related to the positivity property of the Green's functions for certain classes of boundary value problems for a fourth-order equation on a graph. A maximum principle for a fourth-order equation on a graph is formulated, and some properties of differential inequalities are proved.

引用

页码：1731 / 1770

页数：40

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