On the Global Existence and Boundedness of Solutions of a Certain Integro-Vector Differential Equation of Second Order

Cemil Tunc (Department of Mathematics, Faculty of Sciences, Yuzuncu Yil University, Van 65080)
Timur Ayhan (Department of Mathematics, Faculty of Sciences, Yuzuncu Yil University, Van 65080)

Journal of Mathematical and Fundamental Sciences
Vol. 50 No. 1 (2018)

In this paper, we consider a nonlinear integro-vector differential equation of the second order. We establish sufficient conditions that guarantee the global existence and boundedness of solutions of the equation considered. The method of proof involves constructing a suitable Lyapunov functional that gives meaningful results for the problem to be investigated. The result obtained is new and complements that found in the literature. We give an example to verify the result obtained and for illustration purposes. Using MATLAB-Simulink, the behaviors of the orbits of the equation considered are clearly shown.