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

TUNÇ, Cemil; Ayhan, Timur

doi:10.5614/j.math.fund.sci.2018.50.1.1

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

Atıf İçin Kopyala

TUNÇ C., Ayhan T.

JOURNAL OF MATHEMATICAL AND FUNDAMENTAL SCIENCES, cilt.50, sa.1, ss.1-12, 2018 (ESCI)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 50 Sayı: 1
Basım Tarihi: 2018
Doi Numarası: 10.5614/j.math.fund.sci.2018.50.1.1
Dergi Adı: JOURNAL OF MATHEMATICAL AND FUNDAMENTAL SCIENCES
Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
Sayfa Sayıları: ss.1-12
Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.