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Article Citation - WoS: 3Instability Intervals of a Hill's Equation With Piecewise Constant and Alternating Coefficient(Pergamon-elsevier Science Ltd, 2004) Guseinov, GS; Karaca, IYIn this paper, we obtain asymptotic formulas for eigenvalues of the periodic and the semiperiodic boundary value problems associated with a Hill's equation having piecewise constant and alternating coefficient. As a corollary, it is shown that the lengths of instability intervals of the considered Hill's equation tend to infinity. (C) 2004 Elsevier Ltd. All rights reserved.Article Citation - WoS: 43Citation - Scopus: 43Stability Criteria for Linear Periodic Impulsive Hamiltonian Systems(Academic Press inc Elsevier Science, 2007) Guseinov, G. Sh.; Zafer, A.In this paper we obtain stability criteria for linear periodic impulsive Hamiltonian systems. A Lyapunov type inequality is established. Our results improve also the ones previously obtained for systems without impulse effect. (c) 2007 Elsevier Inc. All rights reserved.Article Citation - WoS: 13Citation - Scopus: 15Stability Criterion for Second Order Linear Impulsive Differential Equations With Periodic Coefficients(Wiley-v C H verlag Gmbh, 2008) Guseinov, G. Sh.; Zafer, A.In this paper we obtain instability and stability criteria for second order linear impulsive differential equations with periodic coefficients. Further, a Lyapunov type inequality is also established. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.Article Citation - WoS: 1Citation - Scopus: 2On the Dynamics of the Nonlinear Difference Equation xn+1 = Α Plus Βxn-1 + xn-1(Science Society Thailand, 2015) Aksoy, Aycan; Turan, MehmetThe boundedness and semi-cycle analysis of positive solutions, existence of period-2 solutions, and local and global asymptotic stability of the recursive sequence x(n+1) = alpha + beta x(n-1) + x(n-1)/x(n), n = 0,1,... are investigated where alpha is an element of [0, infinity), beta is an element of [0, 1) and the initial conditions x(-1) and x(0) are arbitrary positive real numbers. The paper concludes with some numerical examples to illustrate the theoretical results.Article Citation - WoS: 79Citation - Scopus: 86Lyapunov inequalities for discrete linear Hamiltonian systems(Pergamon-elsevier Science Ltd, 2003) Guseinov, GS; Kaymakçalan, BIn this paper, we present some Lyapunov type inequalities for discrete linear scalar Hamiltonian systems when the coefficient c(t) is not necessarily nonnegative valued and when the end-points are not necessarily usual zeros, but rather, generalized zeros. Applying these inequalities, we obtain some disconjugacy and stability criteria for discrete Hamiltonian systems. (C) 2003 Elsevier Science Ltd. All rights reserved.
