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Öğe A NOTE ON THE CONTINUABILITY AND BOUNDEDNESS OF SOLUTIONS TO A CLASS OF VECTOR DIFFERENTIAL EQUATIONS OF THIRD ORDER WITH FINITE DELAY(Natl Inquiry Services Centre Pty Ltd, 2017) Ayhan, TimurIn this article, we use Lyapunov's second (or direct) method, by building an appropriate Lyapunov functional. Su?cient conditions which warrant the continuability and boundedness of all solutions to a kind of nonlinear vector differential equations of third order with constant retarded argument are established. Also, we give an example to describe the theoretical analysis in this study and to check the impressiveness of the method employed.Öğe Global existence and boundedness of a certain nonlinear vector integro-differential equation of second order with multiple deviating arguments(Univ Osijek, Dept Mathematics, 2017) Ayhan, Timur; Sofuoglu, YusufIn this study, we consider a vector integro-differential equation with multiple deviating arguments. Based on the Lyapunov-Krasovskii functional approach, the global existence and boundedness of all solutions are discussed. We give an example to illustrate the theoretical analysis made in this study and to show the effectiveness of the method used here.Öğe Global existence and boundedness of solutions for a type of nonlinear integro-differential equations of third order(Balkan Society of Geometers, 2017) Ayhan, Timur; Acan, OmerIn this article, we consider a particular nonlinear integro- differential equation of the third order and discuss the continuability and boundedness of solutions of this equation. Lyapunov's second method is used in the proof of the main theorem by building an appropriate Lya- punov function. The result obtained in this paper contains and improves some well known results on the third order nonlinear integro-differential equations in literature. We also provide an example to illustrate the method. © Balkan Society of Geometers, Geometry Balkan Press 2017.Öğe 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, TimurIn 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.Öğe 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, CemilIn 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.
