OSCILLATORY CRITERIA FOR THE SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS

被引：5

作者：

Grigorian, Gevorg A. ^{[1
]}

机构：

[1] NAS Armenia, Inst Math, Str M Bagramian 24-5,0019 C, Yerevan, Armenia

来源：

MATHEMATICA SLOVACA | 2019年 / 69卷 / 04期

关键词：

Riccati equation; Mathieu equation; normal and extremal solutions; interval and integral oscillatory criteria;

D O I：

10.1515/ms-2017-0274

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Riccati equation method is used to establish three new oscillatory criteria for the second order linear ordinary differential equations. We show that the first of these criteria in the continuous case of the coefficient function (potential) of the equation implies the J. Deng's oscillatory criterion. An extremal oscillatory condition for the Mathieu's equation is obtained. The obtained results are compared with some known oscillatory criteria. (C) 2019 Mathematical Institute Slovak Academy of Sciences

引用

页码：857 / 870

页数：14

共 50 条

[1] ON ONE OSCILLATORY CRITERION FOR THE SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS
Grigorian, Gevorg Avagovich
[J]. OPUSCULA MATHEMATICA, 2016, 36 (05) : 589 - 601
[2] Boundedness and Stability Criteria for Linear Ordinary Differential Equations of the Second Order
Grigoryan, G. A.
[J]. RUSSIAN MATHEMATICS, 2013, 57 (12) : 8 - 15
[3] Interval criteria for oscillation of second-order linear ordinary differential equations
Kong, Q
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 229 (01) : 258 - 270
[4] Oscillation Criteria for Second Order Ordinary Differential Equations
Naito, Manabu
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2020, 63 (02): : 276 - 286
[5] Interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential
Yang, QG
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2003, 135 (01) : 49 - 64
[6] ON AN EXAMPLE IN SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS
WILLETT, D
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 17 (06) : 1263 - &
[7] Oscillatory Periodic Solutions of Nonlinear Second Order Ordinary Differential Equations
Yong Xiang Li
[J]. Acta Mathematica Sinica, 2005, 21 : 491 - 496
[8] Oscillatory Periodic Solutions of Nonlinear Second Order Ordinary Differential Equations
Yong Xiang LI
[J]. Acta Mathematica Sinica,English Series, 2005, 21 (03) : 491 - 496
[9] Oscillatory periodic solutions of nonlinear second order ordinary differential equations
Li, YX
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2005, 21 (03) : 491 - 496
[10] Oscillation criteria for second-order half-linear ordinary differential equations with damping
Li, WT
Zhong, CK
Fan, XL
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2003, 33 (03) : 927 - 951

← 1 2 3 4 5 →