Periodic behaviour of solution for a kind of third-order neutral delay differential equation | ||
| New Valley University Journal of Basic and Applied Sciences | ||
| Articles in Press, Accepted Manuscript, Available Online from 29 May 2022 | ||
| Document Type: Original papers | ||
| DOI: 10.21608/nujbas.2022.114490.1003 | ||
| Authors | ||
| Ayman Mohammed Mahmoud1; Doaa Ali Mohamed Bakhit* 2 | ||
| 1Department of Mathematics, Faculty of Science, New Valley University | ||
| 2Department of Mathematics, Faculty of Science, New Valley University, Egypt, El-Khargah. | ||
| Abstract | ||
| In the present paper, we establish sufficient conditions for the existence and uniqueness of T−periodic solution for a kind of the third-order neutral delay differential equation as the following (x(t) − αx(t − σ))''' + φ(t, x' (t))x ''(t) + ψ1(x(t − r(t)))x' (t) + ψ2(t, x(t − r(t))) = p(t), where T > 0, T−periodic in their first argument , α and σ are constants with |α| < 1. Here, we introduce sufficient conditions for the existence and uniqueness of periodic solution. Our approach is based on the continuation theorem of Mawhin’s coincidence degree theory and analysis technique. The results obtained in this investigation extend many existing and exciting results on nonlinear third-order delay differential equation. Our results improve and form a complement to some results that can be found in the literature. An example is given to illustrate the the importance of the topic and the main results obtained. | ||
| Keywords | ||
| Periodic solution; existence and uniqueness; third-order neutral delay differential equation (NDDEs) | ||
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