7 results
Search Results
Now showing 1 - 7 of 7
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: 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: 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.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.
