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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: 35Citation - Scopus: 43Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives(Springer, 2018) Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; Jarad, Fahd; Ozbekler, AbdullahWe state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.Article Citation - WoS: 3Citation - Scopus: 3Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales(Springer-verlag Italia Srl, 2017) Agarwal, Ravi P.; Cetin, Erbil; Ozbekler, AbdullahIn this paper, we present some newHartman and Lyapunov inequalities for second-order forced dynamic equations on time scales T with mixed nonlinearities: x(Delta Delta)(t) + Sigma(n)(k=1) qk (t)vertical bar x(sigma) (t)vertical bar (alpha k-1) x(sigma) (t) = f (t); t is an element of [t(0), infinity)(T), where the nonlinearities satisfy 0 < alpha(1) < ... < alpha(m) < 1 < alpha(m+1) < ... < alpha(n) < 2. No sign restrictions are imposed on the potentials qk, k = 1, 2, ... , n, and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.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.
