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Article Citation - WoS: 38Citation - Scopus: 37On Oscillation of Second Order Neutral Type Delay Differential Equations(Elsevier Science inc, 2004) Sahiner, YOscillation criteria are obtained by using the so called H-method for the second order neutral type delay differential equations of the form (r(t)psi(x(t))z'(t))' + q(t)f(x(sigma(t))) = 0, t greater than or equal to t(0), where z(t) = x(t) +p(t)x(tau(t)), r, p, q, tau, sigma, is an element of C([t(0), infinity), R) and f, psi is an element of C(R, R). The results of the paper contains several results obtained previously as special cases. Furthermore, we are also able to fix an error in a recent paper related to the oscillation of second order nonneutral delay differential equations. (C) 2003 Elsevier Inc. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1Wong Type Oscillation Criteria for Nonlinear Impulsive Differential Equations(Wiley, 2023) Akgol, Sibel D.; Zafer, AgacikWe present Wong-type oscillation criteria for nonlinear impulsive differential equations having discontinuous solutions and involving both negative and positive coefficients. We use a technique that involves the use of a nonprincipal solution of the associated linear homogeneous equation. The existence of principal and nonpricipal solutions was recently obtained by the present authors. As in special cases, we have superlinear and sublinear Emden-Fowler equations under impulse effects. It is shown that the oscillatory behavior may change due to impulses. An example is also given to illustrate the importance of the results.Article Citation - WoS: 1Citation - Scopus: 1Forced Oscillation of Sublinear Impulsive Differential Equations Via Nonprincipal Solution(Wiley, 2018) Mostepha, Naceri; Ozbekler, AbdullahIn this paper, we give new oscillation criteria for forced sublinear impulsive differential equations of the form (r(t)x')' + q(t)vertical bar x vertical bar(gamma-1) x = f(t), t not equal theta(i); Delta r(t)x' + q(i)vertical bar x vertical bar(gamma-1) x = f(i), t = theta(i), where gamma is an element of(0, 1), under the assumption that associated homogenous linear equation (r(t)z')' + q(t)z = 0, t not equal theta(i); Delta r(t)z' + q(i)z = 0, t = theta(i). is nonoscillatory.Article Citation - WoS: 1Citation - Scopus: 1Sub-Linear Oscillations via Nonprincipal Solution(Editura Acad Romane, 2018) Ozbekler, Abdullah; MathematicsIn the paper, we give new oscillation criteria for forced sub-linear differential equations with "oscillatory potentials" under the assumption that corresponding linear homogeneous equation is nonoscillatory.Article Citation - WoS: 3Citation - Scopus: 3Picone Type Formula for Half-Linear Impulsive Differential Equations With Discontinuous Solutions(Wiley-blackwell, 2015) Ozbekler, A.Picone type formula for half-linear impulsive differential equations with discontinuous solutions having fixed moments of impulse actions is derived. Employing the formula, Leighton and Sturm-Picone type comparison theorems as well as several oscillation criteria for impulsive differential equations are obtained. Copyright (c) 2014 John Wiley & Sons, Ltd.Article Citation - WoS: 2Citation - Scopus: 1Oscillation of Impulsive Linear Differential Equations With Discontinuous Solutions(Cambridge University Press, 2023) Doǧru Akgöl,S.Sufficient conditions are obtained for the oscillation of a general form of a linear second-order differential equation with discontinuous solutions. The innovations are that the impulse effects are in mixed form and the results obtained are applicable even if the impulses are small. The novelty of the results is demonstrated by presenting an example of an oscillating equation to which previous oscillation theorems fail to apply. © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.Article Citation - WoS: 4New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations With Nonlinear Neutral Terms(Mdpi, 2021) Grace, Said R.; Alzabut, Jehad; Ozbekler, AbdullahIn the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples.Article Citation - WoS: 17Citation - Scopus: 20Forced Oscillation of Super-Half Impulsive Differential Equations(Pergamon-elsevier Science Ltd, 2007) Oezbekler, A.; Zafer, A.By using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered. (c) 2007 Elsevier Ltd. All rights reserved.Article Citation - Scopus: 1On the Oscillation of Volterra Integral Equations With Positive and Negative Nonlinearities(Wiley-blackwell, 2016) Ozbekler, AbdullahIn the paper, we give new oscillation criteria for Volterra integral equations having different nonlinearities such as superlinearity and sublinearity. We also present some new sufficient conditions for oscillation under the effect of oscillatory forcing term. Copyright (C) 2015 JohnWiley & Sons, Ltd.Article Citation - WoS: 2Citation - Scopus: 2NEW RESULTS FOR OSCILLATORY PROPERTIES OF NEUTRAL DIFFERENTIAL EQUATIONS WITH A p-LAPLACIAN LIKE OPERATOR(Univ Miskolc inst Math, 2020) Bazighifan, O.; Grace, S. R.; Alzabut, J.; Ozbekler, A.Results reported in this paper provide a generalization for some previously obtained results. Based on comparing with the oscillatory behavior of first-order delay equations, we provide new oscillation criteria for the solutions of even-order neutral differential equations with a p-Laplacian like operator. The proposed theorems not only provide totally different approach but also essentially improve a number of results reported in the literature. To demonstrate the advantage of our results, we present two examples.
