Stability of the solutions of nonlinear third order differential equations with multiple deviating arguments

In this paper, with use of Lyapunov functional, we investigate asymptotic stability of solutions of some nonlinear differential equations of third order with delay. Our results include and improve some well-known results in the literature.

Instability in Multi Delay Functional Differential Equations of Fourth Order

A vector functional differential equation of the fourth order with multiple deviating arguments is considered. New sufficient conditions are established to guarantee the instability of the zero solution of the equation to be considered. We give an example to illustrate the subject.

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

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.