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Article Citation - WoS: 19Citation - Scopus: 21Interval Criteria for the Forced Oscillation of Super-Half Differential Equations Under Impulse Effects(Pergamon-elsevier Science Ltd, 2009) Ozbekler, A.; Zafer, A.In this paper, we derive new interval oscillation criteria for a forced super-half-linear impulsive differential equation having fixed moments of impulse actions. The results are extended to a more general class of nonlinear impulsive differential equations. Examples are also given to illustrate the relevance of the results. (C) 2009 Elsevier Ltd. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 4Second Order Oscillation of Mixed Nonlinear Dynamic Equations With Several Positive and Negative Coefficients(Amer inst Mathematical Sciences-aims, 2011) Ozbekler, Abdullah; Zafer, Agacik; MathematicsNew oscillation criteria are obtained for superlinear and sublinear forced dynamic equations having positive and negative coefficients by means of nonprincipal solutions.Article Citation - WoS: 12Citation - Scopus: 11Oscillation Criterion for Half-Linear Differential Equations With Periodic Coefficients(Academic Press inc Elsevier Science, 2012) Dosly, O.; Ozbekler, A.; Simon Hilscher, R.In this paper, we present an oscillation criterion for second order half-linear differential equations with periodic coefficients. The method is based on the nonexistence of a proper solution of the related modified Riccati equation. Our result can be regarded as an oscillatory counterpart to the nonoscillation criterion by Sugie and Matsumura (2008). These two theorems provide a complete half-linear extension of the oscillation criterion of Kwong and Wong (2003) dealing with the Hill's equation. (C) 2012 Elsevier Inc. All rights reserved.Article Citation - WoS: 27Citation - Scopus: 29Oscillation of Solutions of Second Order Mixed Nonlinear Differential Equations Under Impulsive Perturbations(Pergamon-elsevier Science Ltd, 2011) Ozbekler, A.; Zafer, A.New oscillation criteria are obtained for second order forced mixed nonlinear impulsive differential equations of the form (r(t)Phi(alpha)(x'))' + q(t)(Phi)(x) + Sigma(n)(k=1)q(k)(t)Phi beta(k)(x ) = e(t), t not equal theta(I) x(theta(+)(i)) = ajx(theta(+)(i)) = b(i)x'(theta(i)) where Phi(gamma):= ,s vertical bar(gamma-1)s and beta(1) > beta(2) > ... > beta(m) > alpha > beta(m+1)> ... > beta(n) > beta(n) > 0. If alpha = 1 and the impulses are dropped, then the results obtained by Sun and Wong [Y.G. Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007) 549-560] are recovered. Examples are given to illustrate the results. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1Principal and Nonprincipal Solutions of Impulsive Dynamic Equations: Leighton and Wong Type Oscillation Theorems(Springer, 2023) Zafer, A.; Akgol, S. DogruPrincipal and nonprincipal solutions of differential equations play a critical role in studying the qualitative behavior of solutions in numerous related differential equations. The existence of such solutions and their applications are already documented in the literature for differential equations, difference equations, dynamic equations, and impulsive differential equations. In this paper, we make a contribution to this field by examining impulsive dynamic equations and proving the existence of such solutions for second-order impulsive dynamic equations. As an illustration, we prove the famous Leighton and Wong oscillation theorems for impulsive dynamic equations. Furthermore, we provide supporting examples to demonstrate the relevance and effectiveness of the results.Article Citation - WoS: 2Picone Type Formula for Non-Selfadjoint Impulsive Differential Equations With Discontinuous Solutions(Univ Szeged, Bolyai institute, 2010) Ozbekler, 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: 111Citation - Scopus: 124Oscillation of Second-Order Delay Differential Equations on Time Scales(Pergamon-elsevier Science Ltd, 2005) Sahiner, Y.By means of Riccati transformation technique, we establish some new oscillation criteria for a second-order delay differential equation on time scales in terms of the coefficients. (C) 2005 Elsevier Ltd. All rights reserved.Article Citation - WoS: 8Citation - Scopus: 7Leighton and Wong Type Oscillation Theorems for Impulsive Differential Equations(Pergamon-elsevier Science Ltd, 2021) Akgol, S. D.; Zafer, A.We obtain the well-known Leighton and Wong oscillation theorems for a general class of second-order linear impulsive differential equations by making use of the recently established results on the existence of nonprincipal solutions. The results indicate that the oscillation character of solutions may be altered by the impulsive perturbations, which is not the case in most published works. Another difference is that the equations are quite general in the sense that the impulses are allowed to appear on both solutions and their derivatives. Examples are also given to illustrate the importance of the results. (C) 2021 Elsevier Ltd. All rights reserved.Conference Object Citation - WoS: 3Citation - Scopus: 3Forced Oscillation of Second-Order Impulsive Differential Equations With Mixed Nonlinearities(Springer, 2013) Ozbekler, A.; Zafer, A.In this paper we give new oscillation criteria for a class of second-order mixed nonlinear impulsive differential equations having fixed moments of impulse actions. The method is based on the existence of a nonprincipal solution of a related second-order linear homogeneous equation.Article Citation - WoS: 10Citation - Scopus: 11Forced Oscillation of Second-Order Nonlinear Differential Equations With Positive and Negative Coefficients(Pergamon-elsevier Science Ltd, 2011) Ozbekler, A.; Wong, J. S. W.; Zafer, A.In this paper we give new oscillation criteria for forced super- and sub-linear differential equations by means of nonprincipal solutions. (c) 2011 Elsevier Ltd. All rights reserved.
