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Article Citation - WoS: 9Citation - Scopus: 9Nonoscillation and Oscillation of Second-Order Impulsive Differential Equations With Periodic Coefficients(Pergamon-elsevier Science Ltd, 2012) Ozbekler, A.; Zafer, A.In this paper, we give a nonoscillation criterion for half-linear equations with periodic coefficients under fixed moments of impulse actions. The method is based on the existence of positive solutions of the related Riccati equation and a recently obtained comparison principle. In the special case when the equation becomes impulsive Hill equation new oscillation criteria are also obtained. (C) 2011 Elsevier Ltd. All rights reserved.Article On the Oscillation of Discrete Volterra Equations With Positive and Negative Nonlinearities(Rocky Mt Math Consortium, 2018) Ozbekler, AbdullahIn this paper, we give new oscillation criteria for discrete Volterra equations having different nonlinearities such as super-linear and sub-linear cases. We also present some new sufficient conditions for oscillation under the effect of the oscillatory forcing term.Article Citation - Scopus: 5Picone Type Formula for Non-Selfadjoint Impulsive Differential Equations With Discontinuous Solutions(University of Szeged, 2010) Özbekler,A.; Zafer,A.A Picone type formula for second order linear non-selfadjoint impulsive differential equations with discontinuous solutions having fixed moments of impulse actions is derived. Applying the formula, Leighton and Sturm-Picone type comparison theorems as well as several oscillation criteria for impulsive differential equations are obtained.Article Citation - WoS: 4Citation - Scopus: 4Oscillation Criteria for Non-Canonical Second-Order Nonlinear Delay Difference Equations With a Superlinear Neutral Term(Texas State Univ, 2023) Vidhyaa, Kumar S.; Thandapani, Ethiraju; Alzabut, Jehad; Ozbekler, AbdullahWe obtain oscillation conditions for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term. To cope with non-canonical types of equations, we propose new oscillation criteria for the main equation when the neutral coefficient does not satisfy any of the conditions that call it to either converge to 0 or & INFIN;. Our approach differs from others in that we first turn into the non-canonical equation to a canonical form and as a result, we only require one condition to weed out non-oscillatory solutions in order to induce oscillation. The conclusions made here are new and have been condensed significantly from those found in the literature. For the sake of confirmation, we provide examples that cannot be included in earlier works.
