Browsing by Author "Ozbekler, A."
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Conference Object Citation Count: 3Forced Oscillation of Second-Order Impulsive Differential Equations with Mixed Nonlinearities(Springer, 2013) Özbekler, Abdullah; Zafer, A.; MathematicsIn 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 Count: 10Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients(Pergamon-elsevier Science Ltd, 2011) Özbekler, Abdullah; Wong, J. S. W.; Zafer, A.; MathematicsIn 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.Article Citation Count: 19Interval criteria for the forced oscillation of super-half-linear differential equations under impulse effects(Pergamon-elsevier Science Ltd, 2009) Özbekler, Abdullah; Zafer, A.; MathematicsIn 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 Count: 2NEW RESULTS FOR OSCILLATORY PROPERTIES OF NEUTRAL DIFFERENTIAL EQUATIONS WITH A p-LAPLACIAN LIKE OPERATOR(Univ Miskolc inst Math, 2020) Özbekler, Abdullah; Grace, S. R.; Alzabut, J.; Ozbekler, A.; MathematicsResults reported in this paper provide a generalization for some previously obtained results. Based on comparing with the oscillatory behavior of first-order delay equations, we provide new oscillation criteria for the solutions of even-order neutral differential equations with a p-Laplacian like operator. The proposed theorems not only provide totally different approach but also essentially improve a number of results reported in the literature. To demonstrate the advantage of our results, we present two examples.Article Citation Count: 7Nonoscillation and oscillation of second-order impulsive differential equations with periodic coefficients(Pergamon-elsevier Science Ltd, 2012) Özbekler, Abdullah; Zafer, A.; MathematicsIn 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 Count: 10Oscillation criterion for half-linear differential equations with periodic coefficients(Academic Press inc Elsevier Science, 2012) Özbekler, Abdullah; Ozbekler, A.; Simon Hilscher, R.; MathematicsIn 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 Count: 27Oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations(Pergamon-elsevier Science Ltd, 2011) Özbekler, Abdullah; Zafer, A.; MathematicsNew 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 Count: 4Picone type formula for half-linear impulsive differential equations with discontinuous solutions(Wiley-blackwell, 2015) Özbekler, Abdullah; MathematicsPicone 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 Count: 2PICONE TYPE FORMULA FOR NON-SELFADJOINT IMPULSIVE DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS SOLUTIONS(Univ Szeged, Bolyai institute, 2010) Özbekler, Abdullah; Zafer, A.; MathematicsA 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 Count: 20Principal and nonprincipal solutions of impulsive differential equations with applications(Elsevier Science inc, 2010) Özbekler, Abdullah; Zafer, A.; MathematicsWe introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained. The arguments are based on Polya and Trench factorizations as in non-impulsive differential equations, so we first establish these factorizations. Making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations. Examples are provided with numerical simulations to illustrate the relevance of the results. (C) 2010 Elsevier Inc. All rights reserved.Article Citation Count: 6Sturmian theory for second order differential equations with mixed nonlinearities(Elsevier Science inc, 2015) Özbekler, Abdullah; MathematicsIn the paper, Sturmian comparison theory is developed for the pair of second order differential equations; first of which is the nonlinear differential equations (m(t)y')' + s(t)y' + Sigma(n)(i=1)q(i)(t)vertical bar y vertical bar(proportional to j-1)y = 0, with mixed nonlinearities alpha(1) > ... > alpha(m) > 1 > alpha(m+1) > ... > alpha(n), and the second is the non-selfadjoint differential equations (k(t)x')' + r(t)x' + p(t)x = 0. Under the assumption that the solution of Eq. (2) has two consecutive zeros, we obtain Sturm-Picone type and Leighton type comparison theorems for Eq. (1) by employing the new nonlinear version of Picone's formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for Eq. (1). Examples are given to illustrate the relevance of the results. (C) 2015 Elsevier Inc. All rights reserved.