2014
DOI: 10.1016/j.amc.2013.12.128
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Abstract: Abstract. Stability criteria are given for linear periodic Hamiltonian systems with impulse effect. A Lyapunov type inequality and a disconjugacy criterion are also established. The results improve the ones in the literature for such systems.

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Cited by 7 publications
(2 citation statements)
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“…In this section we provide a Lyapunov type inequality to be used for the uniqueness of the inhomogeneous BVP. The obtained inequality is sharper than the one given by the present authors in [20] in the sense that 2| ( )| is replaced by | ( )|. Theorem 1.…”
Section: Lyapunov Type Inequality For Homogeneous Problemmentioning
confidence: 59%
“…In this section we provide a Lyapunov type inequality to be used for the uniqueness of the inhomogeneous BVP. The obtained inequality is sharper than the one given by the present authors in [20] in the sense that 2| ( )| is replaced by | ( )|. Theorem 1.…”
Section: Lyapunov Type Inequality For Homogeneous Problemmentioning
confidence: 59%
“…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%