Browsing by Author "Ayhan, Timur"

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Global Existence and Boundedness of Solutions of a Certain Nonlinear Integro-Differential Equation of Second Order With Multiple Deviating Arguments
(Springer, 2016) Tunc, Cemil; Ayhan, Timur
In this paper, we consider the global existence and boundedness of solutions for a certain nonlinear integro-differential equation of second order with multiple constant delays. We obtain some new sufficient conditions which guarantee the global existence and boundedness of solutions to the considered equation. The obtained result complements some recent ones in the literature. An example is given of the applicability of the obtained result. The main tool employed is an appropriate Lyapunov-Krasovskii type functional.
New Boundedness Results for a Kind of Nonlinear Differential Equations of Third Order
(Eudoxus Press, Llc, 2011) Tunc, Cemil; Ayhan, Timur
We establish some new sufficient conditions which guarantee the boundedness and the uniform ultimate boundedness of the solutions of a kind of nonlinear differential equations of third order. By defining an appropriate Lyapunov function, we prove two new theorems on the subject. Our results generalize and are complement some known boundedness results in the literature.
On the Asymptotic Stability of Equlibrium Point
(2010) Ayhan, Timur; Tunç, Cemil
Bu çalışma, dört bölümden oluşmaktadır. Birinci bölüm GİRİŞ ve KAYNAK BİLDİRİŞLERİ ile ilgili bilgileri içermektedir.Çalışmanın ikinci bölümünde ise diferansiyel denklemler ve tez konusu ile yakın ilgisi olduğu varsayılan bazı temel bilgiler ve ayrıca konu ile ilgili olarak örnekler verilmektedir.Üçüncü bölümde ise belli türden otonom olmayan diferansiyel denklem sistemleri için bazı yeni kararlılık kriterleri ve zayıf asimptotik kararlılık kriterleri olduğu iddia edilen çalışmalar incelenmektedir.Son bölümde ise yüksek basamaktan lineer olmayan diferansiyel denklemler için çözümlerin bazı davranışları ve Liapunov fonksiyonunun oluşturulması ile ilgili çalışmalar ele alınmaktadır.Anahtar kelimeler: Kararlılık, Asimptotik kararlılık, Liapunov fonksiyonu, Lineer olmayan diferensiyel denklemler.
On the Global Existence and Boundedness of Solutions of a Certain Integro-Vector Differential Equation of Second Order
(inst Teknologi Bandung, 2018) Tunc, Cemil; Ayhan, Timur
In this paper, we consider a nonlinear integro-vector differential equation of the second order. We establish sufficient conditions that guarantee the global existence and boundedness of solutions of the equation considered. The method of proof involves constructing a suitable Lyapunov functional that gives meaningful results for the problem to be investigated. The result obtained is new and complements that found in the literature. We give an example to verify the result obtained and for illustration purposes. Using MATLAB-Simulink, the behaviors of the orbits of the equation considered are clearly shown.
On the Global Existence and Boundedness of Solutions of Nonlinear Vector Differential Equations of Third Order
(Prairie View A & M Univ, dept Mathematics, 2016) Ayhan, Timur; Tunc, Cemil
In this paper, we give some criteria to ensure the global existence and boundedness of solutions to a kind of third order nonlinear vector differential equations. By using the Lyapunov's direct method, we obtain a new result on the topic and give an example for the illustrations. Our result includes, completes and improves some earlier results in the literature.