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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: 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: 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 - 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.
