On the stability and behavior of solutions in mixed differential equations with delays and advances. (12th January 2022)

• Record Type: Journal Article
• Authors: Yeniçerioğlu, Ali Fuat; Yazıcı, Cüneyt; Pinelas, Sandra
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 8(2022)
• Page Start: 4468
• Page End: 4496
• Publication Date: 2022-01-12
• Subjects: asymptotic behavior -- characteristic equation -- mixed differential equation -- stability -- zero solution; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8049
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this study, some new results are obtained on asymptotic behavior and stability analysis of the mixed type differential equation x ′ t = ∫ − 1 0 x t − r 1 θ dv θ + ∫ − 1 0 x t + r 2 θ dη θ, where x t ∈ ℝ, r 1 θ and r 2 θ are real nonnegative continuous functions on − 1, 0, and v θ and η θ are real valued functions of bounded variation on − 1, 0 . These results were obtained by using an appropriate real root of the characteristic equation. Moreover, by the use of two appropriate distinct real roots of the corresponding characteristic equation, a new result on the behavior of solutions is established. Five examples are also given to illustrate our results. We also presented the application of the obtained results in the special case of constant coefficients and have given three different cases in one example. The results obtained in this article show that real roots play an important role.