On the Qualitative Behaviors of Nonlinear Functional Differential Systems of Third Order
In this paper , the author gives new sufficient conditions for the boundedness and globally asymptotically stability of solutions to certain nonlinear delay functional differential systems of third order. The technique of proof involves defining an approp
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On the Qualitative Behaviors of Nonlinear Functional Differential Systems of Third Order Cemil Tunç
Abstract In this paper, the author gives new sufficient conditions for the boundedness and globally asymptotically stability of solutions to certain nonlinear delay functional differential systems of third order. The technique of proof involves defining an appropriate Lyapunov–Krasovskii functional and applying LaSalle’s invariance principle. The obtained results include and improve the results in literature.
11.1 Introduction Ordinary and functional differential equations are frequently encountered as mathematical models arisen from a variety of applications including control systems, electrodynamics, mixing liquids, medicine, biomathematics, economics, atomic energy, information theory, neutron transportation and population models, etc. In addition, it is well known that ordinary and functional differential equations of third order play extremely important and useful roles in many scientific areas such as atomic energy, biology, chemistry, control theory, economy, engineering, information theory, biomathematics, mechanics, medicine, physics, etc. For example, the readers can find applications such as nonlinear oscillations in Afuwape et al. [8], Andres [11], Fridedrichs [19], physical applications in Animalu and Ezeilo [12], nonresonant oscillations in Ezeilo and Onyia [17], prototypical examples of complex dynamical systems in a high-dimensional phase space, displacement in a mechanical system, velocity, acceleration in Chlouverakis and Sprott [14], Eichhorn et al. [16] and Linz [25], the biological model and other models in Cronin- Scanlon [15], electronic theory in Rauch [32], problems in biomathematics in Chlouverakis and Sprott [14] and Smith [36], etc. Qualitative properties of solutions of ordinary and functional equations of third order such as stability, instability, oscillation, boundedness, and periodicity of solutions have been studied by many authors; in this regard, we refer the reader to the monograph by Reissig et al. [33], and the papers of Adams et al. [1], Ademola and C. Tunç (B) Department of Mathematics, Yüzüncü Yıl University, 65080 Van, Turkey e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 J. Bana´s et al. (eds.), Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness, DOI 10.1007/978-981-10-3722-1_11
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Arawomo [2–5], Ademola et al. [6], Afuwape and Castellanos [7], Afuwape and Omeike [9], Ahmad and Rao [10], Bai and Guo [13], Ezeilo and Tejumola [18], Graef et al. [20, 21], Graef and Tunç [22], Kormaz and Tunç [24], Mahmoud and Tunç [26], Ogundare [27], Ogundare et al. [28], Olutimo [29], Omeike [30], Qian [31], Remili and Oudjedi [34], Sadek [35], Swick [37], Tejumola and Tchegnani [38], Tunç [39]–[57], Tunç and Ates [58], Tunç and Gozen [59], Tunç and Mohammed [60], Tunç and Tunç [61], Tunç [62, 63], Zhang and Yu [65], Zhu [66], and theirs references. However, to the best of our knowledge from the literature, by this time, a li
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