On two comparison tests for linear second-order ordinary differential equations

被引：0

作者：

G. A. Grigoryan

机构：

[1] National Academy of Sciences,Institute of Mathematics

来源：

Differential Equations | 2011年 / 47卷

关键词：

Comparison Test; Russian Translation; Riccati Equation; Mathieu Equation; Minorant Equation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove two comparison tests for second-order linear differential equations. The well-known Sturm comparison theorem is a straightforward corollary of the first of them. The second (integral) test permits one to use specific integral relations between the coefficients of two equations to prove the oscillation of one of the equations assuming the oscillation of the other.

引用

页码：1237 / 1252

页数：15

共 50 条

[1] On Two Comparison Tests for Linear Second-Order Ordinary Differential Equations
Grigoryan, G. A.
DIFFERENTIAL EQUATIONS, 2011, 47 (09) : 1237 - 1252
[2] ON OSCILLATION OF SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS
Lomtatidze, A.
Sremr, J.
MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2011, 54 : 69 - 81
[3] Symmetries and invariants of the systems of two linear second-order ordinary differential equations
Bagderina, Yulia Yu.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (10) : 3513 - 3522
[4] Symmetry breaking for a system of two linear second-order ordinary differential equations
Wafo Soh C.
Mahomed F.M.
Nonlinear Dynamics, 2000, 22 (01) : 121 - 133
[5] Linear connections for systems of second-order ordinary differential equations
Crampin, M
Martinez, E
Sarlet, W
ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE, 1996, 65 (02): : 223 - 249
[6] Complete group classification of systems of two linear second-order ordinary differential equations
Moyo, S.
Meleshko, S. V.
Oguis, G. F.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2013, 18 (11) : 2972 - 2983
[7] Group Classification of Systems of Two Linear Second-Order Stochastic Ordinary Differential Equations
Mkhize, T. G.
Oguis, G. F.
Govinder, K.
Moyo, S.
Meleshko, S., V
MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (SYMMETRY 2019), 2019, 2153
[8] BOUNDEDNESS OF A CLASS OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS AND SECOND-ORDER DIFFERENTIAL EQUATIONS WITH DELAY
温立志
ScienceBulletin, 1985, (08) : 1005 - 1008
[9] Nonclassical behavior of solutions of linear second-order ordinary differential equations
Yakubov, V. Ya.
DIFFERENTIAL EQUATIONS, 2008, 44 (01) : 71 - 76
[10] On periodic solutions of linear degenerate second-order ordinary differential equations
V. A. Eremenko
Ukrainian Mathematical Journal, 1997, 49 (8) : 1279 - 1285

← 1 2 3 4 5 →