On boundedness, square integrability and uniform stability for neutral non autonomous third order differential equations with delay
Fatima Abdellaoui, Mebrouk Rahmane
Received January 2, 2024. Published online November 8, 2024.
Abstract: In the study of the solutions for a given class of neutral third order differential equations with delay, a suitable conditions are given based on the Lyapunov second method by considering convenable Lyapunov functional to guarantee the uniform asymptotic stability, the boundedness and the square integrability.
Keywords: asymptotic stability; square integrability; Lyapunov functional; non autonomous differential equation of third order with delay
References: [1] R. P. Agarwal, D. O'Regan: Singular problems modelling phenomena in the theory of pseudoplastic fluids. ANZIAM J. 45 (2003), 167-179. DOI 10.1017/S1446181100013249 | MR 2017741 | Zbl 1201.35155
[2] D. Beldjerd, M. Remili: Boundedness and square integrability of solutions of certain third-order differential equations. Math. Bohem. 143 (2018), 377-389. DOI 10.21136/MB.2018.0029-17 | MR 3895262 | Zbl 1463.34151
[3] J. R. Graef, D. Beldjerd, M. Remili: On stability, boundedness, and square integrability of solutions of certain third order neutral differential equations. Math. Bohem. 147 (2022), 285-299. DOI 10.21136/MB.2021.0081-19 | MR 4482306 | Zbl 1524.34179
[4] J. Hale: Theory of Functional Differential Equations. Applied Mathematical Sciences 3. Springer, New York (1977). DOI 10.1007/978-1-4612-9892-2 | MR 0508721 | Zbl 0352.34001
[5] D. J. O'Regan: Topological transversality: Applications to third order boundary value problems. SIAM. J. Math. Anal. 18 (1987), 630-641. DOI 10.1137/0518048 | MR 0883557 | Zbl 0628.34017
[6] L. D. Oudjedi, B. Lekhmissi, M. Remili: Asymptotic properties of solutions to third order neutral differential equations with delay. Proyecciones 38 (2019), 111-127. DOI 10.4067/S0716-09172019000100111 | MR 3915244 | Zbl 1447.34065
[7] M. Rahmane, M. Remili: On stability and boundedness of solutions of certain non autonomous fourth-order delay differential equations. Acta Univ. M. Belii, Ser. Math. 23 (2015), 101-114. MR 3373833 | Zbl 1344.34078
[8] M. Rahmane, M. Remili, L. D. Oudjedi: Boundedness and square integrability in neutral differential systems of fourth order. Appl. Appl. Math. 14 (2019), 1215-1231. MR 4044174 | Zbl 1433.34053
[9] M. Remili, L. D. Oudjedi: On asymptotic stability of solutions to third order nonlinear delay differential equation. Filomat 30 (2016), 3217-3226. DOI 10.2298/FIL1612217R | MR 3593070 | Zbl 1474.34508
[10] A. I. Sadek: Stability and boundedness of a kind of third-order delay differential system. Appl. Math. Lett. 16 (2003), 657-662. DOI 10.1016/S0893-9659(03)00063-6 | MR 1986031 | Zbl 1056.34078
[11] Y. Sun, Y. Zhao: Oscillation and asymptotic behavior of third-order nonlinear neutral delay differential equations with distributed deviating arguments. J. Appl. Anal. Comput. 8 (2018), 1796-1810. DOI 10.11948/2018.1796 | MR 3884389 | Zbl 1464.34089
[12] C. Tunc: Stability and boundedness in differential systems of third order with variable delay. Proyecciones 35 (2016), 317-338. DOI 10.4067/S0716-09172016000300008 | MR 3552443 | Zbl 1384.34082
[13] Z. Zhang, J. Wang, W. Shi: A boundary layer problem arising in gravity-driven laminar film flow of power-law fluids along vertical walls. Z. Angew. Math. Phys. 55 (2004), 169-780. DOI 10.1007/s00033-004-1122-7 | MR 2087764 | Zbl 1059.76007
Affiliations: Fatima Abdellaoui, Mebrouk Rahmane (corresponding autor), Laboratory of Mathematics, Modelisation and Applications (LaMMA), University Ahmed Draia of Adrar, Adrar, Algeria, e-mail: abdellaouifatima11@gmail.com, meb.rahmane@univ-adrar.edu.dz
