Akgöl, Sibel Doğru
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Akgol, S. Dogru
Akgol, Sibel D.
Akgol,S.D.
S.D.Akgol
A.,Sibel Dogru
Akgöl,S.D.
S.,Akgöl
Akgol, Sibel Dogru
A.,Sibel Doğru
A., Sibel Dogru
Akgöl, Sibel Doğru
S., Akgol
Sibel Dogru, Akgol
Sibel Doğru, Akgöl
S.D.Akgöl
Akgol, Sibel D.
Akgol,S.D.
S.D.Akgol
A.,Sibel Dogru
Akgöl,S.D.
S.,Akgöl
Akgol, Sibel Dogru
A.,Sibel Doğru
A., Sibel Dogru
Akgöl, Sibel Doğru
S., Akgol
Sibel Dogru, Akgol
Sibel Doğru, Akgöl
S.D.Akgöl
Job Title
Doktor Öğretim Üyesi
Email Address
sibel.dogruakgol@atilim.edu.tr
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Scholarly Output
13
Articles
11
Citation Count
14
Supervised Theses
1
13 results
Scholarly Output Search Results
Now showing 1 - 10 of 13
Article Citation Count: 0DE LA VALLEE POUSSIN INEQUALITY FOR IMPULSIVE DIFFERENTIAL EQUATIONS(Walter de Gruyter Gmbh, 2021) Akgöl, Sibel Doğru; Özbekler, Abdullah; MathematicsThe de la Vallee Poussin inequality is a handy tool for the investigation of disconjugacy, and hence, for the oscillation/nonoscillation of differential equations. The results in this paper are extensions of former those of Hartman and Wintner [Quart. Appl. Math. 13 (1955), 330-332] to the impulsive differential equations. Although the inequality first appeared in such an early date for ordinary differential equations, its improved version for differential equations under impulse effect never has been occurred in the literature. In the present study, first, we state and prove a de la Vallee Poussin inequality for impulsive differential equations, then we give some corollaries on disconjugacy. We also mention some open problems and finally, present some examples that support our findings. (C) 2021 Mathematical Institute Slovak Academy of SciencesArticle Citation Count: 0Existence of solutions for first order impulsive periodic boundary value problems on time scales(Univ Nis, Fac Sci Math, 2023) Akgöl, Sibel Doğru; Akgol, Sibel Dogru; Kus, M. Eymen; MathematicsIn this paper we study a class of first order impulsive periodic boundary value problems on time scales. We give conditions under which the considered problem has at least one and at least two solutions. The arguments are based upon recent fixed point index theory in cones of Banach spaces for a k-set contraction perturbed by an expansive operator. An example is given to illustrate the obtained result.Article Citation Count: 1EXISTENCE OF SOLUTIONS FOR THIRD ORDER MULTI POINT IMPULSIVE BOUNDARY VALUE PROBLEMS ON TIME SCALES(Univ Miskolc inst Math, 2022) Akgöl, Sibel Doğru; Akgol, Sibel D.; Kus, M. Eymen; MathematicsIn this paper, we obtain sufficient conditions for existence of solutions of a third order m-point impulsive boundary value problem on time scales. To the best of our knowledge, there is hardly any work dealing with third order multi point dynamic impulsive BVPs. The reason may be the complex arguments caused by both impulsive perturbations and calculations on time scales. As an application, we give an example demonstrating our results.Article Citation Count: 0EXISTENCE OF SOLUTIONS FOR IMPULSIVE BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS(Ankara Univ, Fac Sci, 2023) Doğru Akgöl, Sibel; Akgöl, Sibel Doğru; Akgöl, Sibel Doğru; MathematicsThe paper deals with the existence of solutions for a general class of second-order nonlinear impulsive boundary value problems defined on an infinite interval. The main innovative aspects of the study are that the results are obtained under relatively mild conditions and the use of principal and nonprincipal solutions that were obtained in a very recent study. Additional results about the existence of bounded solutions are also provided, and theoretical results are supported by an illustrative example.Article Citation Count: 1Wong type oscillation criteria for nonlinear impulsive differential equations(Wiley, 2023) Akgöl, Sibel Doğru; Zafer, Agacik; MathematicsWe present Wong-type oscillation criteria for nonlinear impulsive differential equations having discontinuous solutions and involving both negative and positive coefficients. We use a technique that involves the use of a nonprincipal solution of the associated linear homogeneous equation. The existence of principal and nonpricipal solutions was recently obtained by the present authors. As in special cases, we have superlinear and sublinear Emden-Fowler equations under impulse effects. It is shown that the oscillatory behavior may change due to impulses. An example is also given to illustrate the importance of the results.Master Thesis Zaman skalalarında yüksek mertebeden çok noktalı impalsif sınır değer problemlerinin çözümlerinin varlığı(2022) Akgöl, Sibel Doğru; Akgöl, Sibel Doğru; Georgıev, Svetlin G.; MathematicsBu tezde, çok noktalı yüksek mertebeden impalsif sınır değer problemlerinin zaman skalalarında çözümlerinin bulunması için yeterli koşulları araştırdık. Özellikle, üçüncü mertebeden impalsif sınır değer problemlerinin bir sınıfı ve 2n + 1, n ≥ 1 mertebeden bir impalsif sınır değer problemi sınıfı incelenmiştir. Bölüm 1'de zaman skalası ve bazı ilgili kavramların tanımları ile birlikte örnekler verilmiştir. Sonrasında tezde kullanılan sabit nokta teoremleri verilmiştir. Bölüm 2, üçüncü mertebeden çok noktalı dinamik impalsif sınır değer problemlerinin çözümlerinin varlığına ayrılmıştır. Bölüm 3'de tek sayı mertebeli çok noktalı dinamik impalsif sınır değer problemlerinin çözümlerinin varlığına odaklanılmıştır. Son olarak, Bölüm 4'te kısa bir sonuc¸ verilmiştir. Bu tezdeki sonuçların bir kısmı Georgian Mathematical Journal dergisinde basılmış, bir kısmı da Miskolc Mathematical Notes dergisinde basılmak üzere kabul edilmiştir.Book Part Citation Count: 0De La Vallée Poussin-type inequality for impulsive dynamic equations on time scales(De Gruyter, 2023) Akgöl, Sibel Doğru; Özbekler, Abdullah; MathematicsWe derive a de La Vallée Poussin-type inequality for impulsive dynamic equations on time scales. This inequality is often used in conjunction with disconjugacy and/or (non)oscillation. Hence, it appears to be a very useful tool for the qualitative study of dynamic equations. In this work, generalizing the classical de La Vallée Poussin inequality for impulsive dynamic equations on arbitrary time scales, we obtain a dis-conjugacy criterion and some results on nonoscillation. We also present illustrative examples that support our findings. © 2023 Walter de Gruyter GmbH, Berlin/Bostonl. All rights reserved.Article Citation Count: 6Prescribed asymptotic behavior of second-order impulsive differential equations via principal and nonprincipal solutions(Academic Press inc Elsevier Science, 2021) Akgöl, Sibel Doğru; Zafer, A.; MathematicsFinding 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 Count: 3Asymptotic representation of solutions for second-order impulsive differential equations(Elsevier Science inc, 2018) Akgöl, Sibel Doğru; Zafer, A.; MathematicsWe 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 Count: 0Asymptotic equivalence of impulsive dynamic equations on time scales(Hacettepe Univ, Fac Sci, 2023) Akgöl, Sibel Doğru; MathematicsThe asymptotic equivalence of linear and quasilinear impulsive dynamic equations on time scales, as well as two types of linear equations, are proven under mild conditions. To establish the asymptotic equivalence of two impulsive dynamic equations a method has been developed that does not require restrictive conditions, such as the boundedness of the solutions. Not only the time scale extensions of former results have been obtained, but also improved for impulsive differential equations defined on the real line. Some illustrative examples are also provided, including an application to a generalized Duffing equation.
