Open AccessStability, boundedness and existence of unique periodic solutions to a class of fourth order functional differential equations
Author(s) -
A. T. Ademola
Publication year - 2021
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-2021-02-0017
Subject(s) - mathematics , class (philosophy) , differential equation , order (exchange) , stability (learning theory) , mathematical analysis , exponential stability , nonlinear system , computer science , physics , finance , quantum mechanics , artificial intelligence , machine learning , economics
In this paper a novel class of fourth order functional differential equations is discussed. By reducing the fourth order functional differential equation to system of first order, a suitable complete Lyapunov functional is constructed and employed to obtain sufficient conditions that guarantee existence of a unique periodic solution, asymptotic and uniform asymptotic stability of the zero solutions, uniform boundedness and uniform ultimate boundedness of solutions. The obtained results are new and include many prominent results in literature. Finally, two examples are given to show the feasibility and reliability of the theoretical results.