Stability, Boundedness, and Existence of Periodic Solutions to Certain Third‐Order Delay Differential Equations with Multiple Deviating Arguments

AT Ademola, BS Ogundare… - International Journal …, 2015 - Wiley Online Library
International Journal of Differential Equations, 2015Wiley Online Library
The behaviour of solutions for certain third‐order nonlinear differential equations with
multiple deviating arguments is considered. By employing Lyapunov's second method, a
complete Lyapunov functional is constructed and used to establish sufficient conditions that
guarantee existence of unique solutions that are periodic, uniformly asymptotically stable,
and uniformly ultimately bounded. Obtained results not only are new but also include many
outstanding results in the literature. Finally, the correctness and effectiveness of the results …
The behaviour of solutions for certain third‐order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results not only are new but also include many outstanding results in the literature. Finally, the correctness and effectiveness of the results are justified with examples.
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