Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article An Exponential Estimate for Solutions of Linear Impulsive Delay Differential Equations(Academic Publication Council, 2007) Alzabut, Jehad; Alzabut, Jehad; Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikThis paper is concerned with linear impulsive delay differential equations with impulsive conditions allowing delays in the index of the jumps. We obtain an exponential estimate for the solutions of such types of equations. In preparation to this, we present three essential lemmas related to the adjoint equation, the representation of solutions and a bound for the fundamental matrix. Moreover, a sharper estimate is provided.Article Citation - Scopus: 5A Necessary and Sufficient Condition for the Existence of Periodic Solutions of Linear Impulsive Differential Equations With Distributed Delay(2007) Alzabut, J.O.; Alzabut, Jehad; MatematikA necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive differential equations with distributed delay.Conference Object Oscillation Criteria for Second Order Impulsive Delay Differential Equation(Amer inst Physics, 2004) Taş, Kenan; Alzabut, J; Zafert, A; Baleanu, Dumitru; MatematikA necessary and sufficient condition is obtained for oscillation of bounded solutions of second order impulsive delay differential equations of the form (r(t)x(t))'+p(t)f(x(i(t)))=0, t not equal theta Delta(r(theta(i))x'(theta(i)))+b(i)g(x(sigma(theta(i)))) = 0, i is an element of Z, Deltax(theta(i)) = 0. An example is also inserted to illustrate the effect of impulses on the oscillatory behavior of the solutions.Book Part A Stability Criterion for Delay Differential Equations With Impulse Effects(World Scientific Publishing Co., 2007) Alzabut, J.O.In this paper, we prove that if a delay differential equation with impulse effects of the form x’(t) = A(t)x(t) + B(t)x(t - τ), t ≠ θi, Δx(θi) = Cix(θi) + Dix(θi-j); i ∈ 2 N; verfies a Perron condition then its trivial solution is uniformly asymptotically stable. © 2007 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.Article Citation - WoS: 35Citation - Scopus: 35On Existence of a Globally Attractive Periodic Solution of Impulsive Delay Logarithmic Population Model(Elsevier Science inc, 2008) Alzabut, Jehad O.; Abdeljawad, ThabetIn this paper, it is shown that a logarithmic population model which is governed by impulsive delay differential equation has a globally attractive periodic solution. (c) 2007 Elsevier Inc. All rights reserved.Article Citation - WoS: 28Citation - Scopus: 33Existence of Periodic Solutions, Global Attractivity and Oscillation of Impulsive Delay Population Model(Pergamon-elsevier Science Ltd, 2007) Alzabut, J. O.; Saker, S. H.In this paper we consider the nonlinear impulsive delay population model. The main objective is to systematically study the qualitative behavior of the model including existence of periodic solutions, global attractivity and oscillation. The main oscillation results are the results of the prevalence of the mature cells about the periodic solutions and the global attractivity results are the conditions for nonexistence of dynamical diseases on the population. (c) 2006 Elsevier Ltd. All rights reserved.Article Citation - WoS: 15Citation - Scopus: 16Periodic Solutions, Global Attractivity and Oscillation of an Impulsive Delay Host-Macroparasite Model(Pergamon-elsevier Science Ltd, 2007) Alzabut, J. O.; Saker, S. H.In this paper we will consider the nonlinear impulsive delay host-macroparasite model with periodic coefficients. By means of the continuation theorem of coincidence degree, we establish a sufficient condition for the existence of a positive periodic solution M(t) with strictly positive components. Moreover, we establish a sufficient condition for the global attractivity of M(t) and some sufficient conditions for oscillation of all positive solutions about the positive periodic solution M(t). (c) 2006 Elsevier Ltd. All rights reserved.Article Citation - WoS: 34Citation - Scopus: 37Perron's Theorem for Linear Impulsive Differential Equations With Distributed Delay(Elsevier Science Bv, 2006) Alzabut, J.; Zafer, A.; Akhmet, M. U.In this paper it is shown that under a Perron condition trivial solution of linear impulsive differential equation with distributed delay is uniformly asymptotically stable. (c) 2005 Elsevier B.V. All rights reserved.