Stability, boundedness and periodic solutions to certain second order delay differential equations.
DOI:
https://doi.org/10.4067/S071609172017000200257Keywords:
Second order, Nonlinear differential equation, Uniform stability, Uniform ultimate boundedness, Existence of a unique periodic solutionsAbstract
Stability, boundedness and existence of a unique periodic solution to certain second order nonlinear delay differential equations is discussed. By employing Lyapunov's direct (or second) method, a complete Lyapunov functional is constructed and used to establish sufficient conditions, on the nonlinear terms, that guarantee uniform asymptotic stability, uniform ultimate boundedness and existence of a unique periodic solution. Obtained results complement many outstanding recent results in the literature. Finally, examples are given to show the effectiveness of our method and correctness of our results.
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