PROPERTIES OF CRITICAL AND SUBCRITICAL SECOND ORDER SELF-ADJOINT LINEAR EQUATIONS

被引：2

作者：

Jekl, Jan ^{[1
]}

机构：

[1] Masaryk Univ, Dept Math & Stat, Kotlarska 2, CZ-61137 Brno, Czech Republic

来源：

MATHEMATICA SLOVACA | 2021年 / 71卷 / 05期

关键词：

critical equation; Riccati equation; difference equation; coefficient delayed equation; DIFFERENCE-EQUATIONS; ASYMPTOTIC-BEHAVIOR; OSCILLATION; GROWTH;

D O I：

10.1515/ms-2021-0045

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss critical and subcritical linear second-order difference equations, and we observe several identities and inequalities which such equations satisfy depending on their coefficients. Later, we investigate the limit behaviour depending on the coefficients of solutions and of the sequences which appear when finding said solutions. We will see that certain identity is preserved in limit under weaker assumptions. Finally, we investigate a class of fourth-order linear difference equations and show that they are always 1-critical. (C) 2021 Mathematical Institute Slovak Academy of Sciences

引用

页码：1149 / 1166

页数：18

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