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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: 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: 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.
