LYAPUNOV-TYPE INEQUALITIES FOR PLANAR LINEAR DYNAMIC HAMILTONIAN SYSTEMS

Download
2013-04-01
Bohner, Martin
Zafer, Ağacık
We give new Lyapunov-type inequalities for linear Hamiltonian systems on arbitrary time scales, which improve recently published results and hence all the related ones in the literature. As an application, we obtain new diconjugacy criteria for linear Hamiltonian systems.
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS

Suggestions

On Lyapunov inequality in stability theory for Hill's equation on time scales
Atici, FM; Guseinov, GS; Kaymakcalan, B (Springer Science and Business Media LLC, 2000-01-01)
In this paper we obtain sufficient conditions for instability and stability to hold for second order linear Delta -differential equations on time scales with periodic coefficients.
Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments
Dahiya, R. S.; Zafer, A. (Springer Science and Business Media LLC, 2007)
We derive oscillation criteria for general-type neutral differential equations [x(t) +αx(t− τ) +βx(t +τ)](n) = δ b ax(t − s)dsq1(t,s) + δ d c x(t + s)dsq2(t,s) = 0, t ≥ t0, where t0 ≥ 0, δ = ±1, τ > 0, b>a ≥ 0, d>c ≥ 0, α and β are real numbers, the functions q1(t,s) : [t0,∞) × [a,b] → R and q2(t,s):[t0,∞) × [c,d] → R are nondecreasing in s for each fixed t, and τ is periodic and continuous with respect to t for each fixed s. In certain special cases, the results obtained generalize and improve s...
Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients
ÖZBEKLER, ABDULLAH; Wong, J. S. W.; Zafer, Ağacık (Elsevier BV, 2011-07-01)
In this paper we give new oscillation criteria for forced super- and sub-linear differential equations by means of nonprincipal solutions.
Nonautonomous Bifurcations in Nonlinear Impulsive Systems
Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01)
In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
Matrix measure approach to Lyapunov-type inequalities for linear Hamiltonian systems with impulse effect
Kayar, Zeynep; Zafer, Ağacık (Elsevier BV, 2016-08-01)
We present new Lyapunov-type inequalities for Hamiltonian systems, consisting of 2n-first-order linear impulsive differential equations, by making use of matrix measure approach. The matrix measure estimates of fundamental matrices of linear impulsive systems are crucial in obtaining sharp inequalities. To illustrate usefulness of the inequalities we have derived new disconjugacy criteria for Hamiltonian systems under impulse effect and obtained new lower bound estimates for eigenvalues of impulsive eigenva...
Citation Formats
M. Bohner and A. Zafer, “LYAPUNOV-TYPE INEQUALITIES FOR PLANAR LINEAR DYNAMIC HAMILTONIAN SYSTEMS,” APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, pp. 129–142, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56649.