On the oscillation of Hill's equations under periodic forcing

被引：7

作者：

Kwong, MK

Wong, JSW

机构：

[1] City Univ Hong Kong, Kowloon, Hong Kong, Peoples R China

[2] Lucent Technol Inc, Lisle, IL 60532 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2006年 / 320卷 / 01期

关键词：

ordinary differential equations; second order; linear; periodic; oscillation;

D O I：

10.1016/j.jmaa.2005.06.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use the Floquet theory of the Hill's equation to prove the conjecture that all solutions of the second order forced linear differential equation y" + c(sin t)y = cos t, are oscillatory on [0, infinity) for all c not equal 0. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：37 / 55

页数：19

共 21 条

[1] ATKINSON FV, 1957, MATH Z, V68, P82
[2] *EINE UMKEHRUNG DER STURM-LIOUVILLESCHEN EIGENWERTAUFGABE - BESTIMMUNG DER DIFFERENTIALGLEICHUNG DURCH DIE EIGENWERTE
BORG, G
[J]. ACTA MATHEMATICA, 1946, 78 (01) : 1 - 96
[3] OSCILLATION THEOREMS FOR A NONLINEAR ANALOG OF HILLS EQUATION
BUTLER, GJ
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1976, 27 (106) : 159 - 171
[4] Chicone C., 1991, ORDINARY DIFFERENTIA
[5] Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein
Clark, S
Hinton, D
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (10) : 3005 - 3015
[6] Coppel W.A., 1971, Lecture Notes in Mathematics, V220
[7] Grimshaw R., 1993, NONLINEAR ORDINARY D
[8] Hartman P., 1973, Ordinary Differential Equations
[9] Hill G.W., 1886, Acta Math, V8, P1, DOI [DOI 10.1007/BF02417081, 10.1007/BF02417081]
[10] Estimates for the Hill operator, I
Korotyaev, E
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 162 (01) : 1 - 26

← 1 2 3 →