Lyapunov-type inequalities for a class of even-order differential equations

Zhang, Qiming; He, Xiaofei

doi:10.1186/1029-242x-2012-5

Cited by 8 publications

(3 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Lyapunov inequality and its generalizations have been used successfully in connection with oscillation and Sturmian theory, asymptotic theory, disconjugacy, eigenvalue problems and various properties of the solutions of (1) and related equations, see for instance [57,29,5,12,13,14,17,18,25,31,35,36,38,39,40,41,44,48,49,50] and the references cited therein. For some of its extensions to Hamiltonian systems, higher order differential equations, nonlinear and half-linear differential equations, difference and dynamic equations, functional and impulsive differential equations, we refer in particular to [17,18,15,16,21,22,23,24,27,28,20,32,34,42,43,45,46,47,51,53,54,55,56,58]. Further, no more Lyapunov and Hartman type inequalities are known for higher-order nonlinear differential equations.…”

Section: Introduction Consider the Hill's Equationmentioning

confidence: 99%

Lyapunov type inequalities for $n$th order forced differential equations with mixed nonlinearities

Agarwal¹,

Özbekler²

2016

CPAA

View full text Add to dashboard Cite

show abstract

Section: Introduction Consider the Hill's Equationmentioning

confidence: 99%

Lyapunov type inequalities for $n$th order forced differential equations with mixed nonlinearities

Agarwal¹,

Özbekler²

2016

CPAA

View full text Add to dashboard Cite

show abstract

“…Such as to nonlinear second order equations, to delay differential equations, to higher order differential equations, to difference equations and to differential and difference systems. See, for example, the references – and the references therein. In , Çakmark considered the following even‐order linear differential equation:

x^{(2 n)} + q (t) x = 0, a \leq t \leq b,

where

q \in C [a, b]

, and

x (t)

satisfies the following boundary conditions

x^{(2 k)} (a) = x^{(2 k)} (b) = 0, k = 0, 1, 2, ..., n - 1 .

He obtained the following result:…”

Section: Introductionmentioning

confidence: 99%

“…Such as to nonlinear second order equations, to delay differential equations, to higher order differential equations, to difference equations and to differential and difference systems. See, for example, the references [1]- [14] and the references therein. In [1], Ç akmark considered the following even-order linear differential equation:…”

Section: Introductionmentioning

confidence: 99%