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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: 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 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: 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.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.
