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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.
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    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.
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    ON THE PERIODIC SOLUTIONS OF NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS VIA FIXED POINT METHOD
    (Univ Prishtines, 2022) Arik, Irem Akbulut; Tunc, Cemil
    In the present article, we study existence of periodic solutions (EPSs) of a nonlinear neutral integro- differential equation (NIDE) with multiple variable delays using Krasnoselskiis fixed point theorem. Transforming the considered NIDE to an equivalent integral equation, we prove the EPSs using a fixed point mapping, which is defined as a sum of a contraction and a compact map. The result of this paper has contributions to the topic of the EPSs of NIDEs.
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    On the stability of solutions of neutral differential equations of first order
    (Lebanese Univ, 2019) Akbulut, Irem; Tunc, Cemil
    In this work, the existence and uniqueness of solutions, boundedness of solutions and stability of zero solution of a specific neutral differential equations of first order with multiple time delays are discussed by the fixed point method. An example is given to show the applicability of the results introduced. By this work, we aim to extend and improve some previous results can be found in the literature and to do a contribution to the subject and the literature.
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    STABILITY OF A LINEAR INTEGRO-DIFFERENTIAL EQUATION OF FIRST ORDER WITH VARIABLE DELAYS
    (Int Center Scientific Research & Studies, 2018) Tunc, Cemil; Akbulut, Irem
    We consider a linear integro-differential equation (IDE) of first order with two variable delays. We construct new conditions guaranteeing the trivial solution of this IDE is stable. The technique of the proof based on the use of the fixed-point theory. Our findings generalize and improve some results can be found in the literature.