Browsing by Author "Zafer, A."
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Article Citation - WoS: 3Citation - Scopus: 3Asymptotic Representation of Solutions for Second-Order Impulsive Differential Equations(Elsevier Science inc, 2018) Akgol, S. Dogru; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityWe obtain sufficient conditions which guarantee the existence of a solution of a class of second order nonlinear impulsive differential equations with fixed moments of impulses possessing a prescribed asymptotic behavior at infinity in terms of principal and nonprincipal solutions. An example is given to illustrate the relevance of the results. (C) 2018 Elsevier Inc. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 3Boundary Value Problems on Half-Line for Second-Order Nonlinear Impulsive Differential Equations(Wiley, 2018) Akgol, S. D.; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityWe obtain sufficient conditions for existence and uniqueness of solutions of boundary value problems on half-line for a class of second-order nonlinear impulsive differential equations. Our technique is different than the traditional ones, as it is based on asymptotic integration method involving principal and nonprincipal solutions. Examples are provided to illustrate the relevance of the results.Conference Object Citation - WoS: 3Citation - Scopus: 3Forced Oscillation of Second-Order Impulsive Differential Equations With Mixed Nonlinearities(Springer, 2013) Ozbekler, A.; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityIn 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: 9Citation - 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.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityIn 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 - WoS: 17Citation - Scopus: 20Forced Oscillation of Super-Half Impulsive Differential Equations(Pergamon-elsevier Science Ltd, 2007) Oezbekler, A.; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityBy using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered. (c) 2007 Elsevier Ltd. All rights reserved.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.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityIn 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: 8Citation - Scopus: 7Leighton and Wong Type Oscillation Theorems for Impulsive Differential Equations(Pergamon-elsevier Science Ltd, 2021) Akgol, S. D.; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityWe 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: 9Citation - Scopus: 9Nonoscillation and Oscillation of Second-Order Impulsive Differential Equations With Periodic Coefficients(Pergamon-elsevier Science Ltd, 2012) Ozbekler, A.; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityIn 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: 27Citation - Scopus: 29Oscillation of Solutions of Second Order Mixed Nonlinear Differential Equations Under Impulsive Perturbations(Pergamon-elsevier Science Ltd, 2011) Ozbekler, A.; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityNew 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.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityA 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: 7Citation - Scopus: 7Prescribed asymptotic behavior of second-order impulsive differential equations via principal and nonprincipal solutions(Academic Press inc Elsevier Science, 2021) Akgol, S. Dogru; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityFinding solutions with prescribed asymptotic behavior is a classical problem for differential equations, which is also known as the asymptotic integration problem for differential equations. Very recent results have revealed that the problem is closely related to principal and nonprincipal solutions of a related homogeneous linear differential equation. Such solutions for second-order linear differential equations without impulse effects, first appeared in [W. Leighton, M. Morse, Trans. Amer. Math. Soc. 40 (1936), 252-286]. In the present work we first establish the concept of principal and nonprincipal solutions for second-order linear impulsive differential equations, and then use them to prove the existence of solutions for a class of second-order nonlinear impulsive differential equations, with prescribed asymptotic behavior at infinity in terms of a linear combination of these principal and nonprincipal solutions. Examples and numerical simulations are provided to illustrate the obtained results. (c) 2021 Elsevier Inc. All rights reserved.Article Citation - WoS: 21Citation - Scopus: 20Principal and Nonprincipal Solutions of Impulsive Differential Equations With Applications(Elsevier Science inc, 2010) Ozbekler, A.; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityWe 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 - WoS: 1Citation - Scopus: 1Principal and Nonprincipal Solutions of Impulsive Dynamic Equations: Leighton and Wong Type Oscillation Theorems(Springer, 2023) Zafer, A.; Akgol, S. Dogru; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityPrincipal 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: 43Citation - Scopus: 43Stability Criteria for Linear Periodic Impulsive Hamiltonian Systems(Academic Press inc Elsevier Science, 2007) Guseinov, G. Sh.; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityIn this paper we obtain stability criteria for linear periodic impulsive Hamiltonian systems. A Lyapunov type inequality is established. Our results improve also the ones previously obtained for systems without impulse effect. (c) 2007 Elsevier Inc. All rights reserved.Article Citation - WoS: 13Citation - Scopus: 15Stability Criterion for Second Order Linear Impulsive Differential Equations With Periodic Coefficients(Wiley-v C H verlag Gmbh, 2008) Guseinov, G. Sh.; Zafer, A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım UniversityIn this paper we obtain instability and stability criteria for second order linear impulsive differential equations with periodic coefficients. Further, a Lyapunov type inequality is also established. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
