ON THE WEIGHTED PSEUDO ALMOST PERIODIC SOLUTIONS FOR LIÉNARD -TYPE SYSTEMS WITH VARIABLE DELAYS

Year 2020, Volume: 6 Issue: 2, 89 - 93, 31.12.2020

Ramazan Yazgan

https://doi.org/10.22531/muglajsci.734586

Cited By: 2

Abstract

This study deals with Liénard-type differential equation systems with time-varying delays. Some sufficient conditions have been obtained for the existence and uniqueness of the weighted pseudo almost periodic solutions of the considered system by using some differential inequalities, the main features of the weighted pseudo almost periodic and Banach Fixed Point Theorem. Since the weighted pseudo almost periodic functions space is more general than the almost and pseudo almost pseudo periodic functions space, this work is a new and complementary. In addition, an example is given to show the correctness of the created conditions.

Keywords

Liénard System, Fixed Point Theorem, Almost Periodic Solution

References

• A. M. Fink; Almost Periodic Differential Equations, vol. 377 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1974.
• C. Zhang; Almost Periodic Type Functions and Ergodicity, Kluwer Academic/Science Press, Beijing, 2003.
• H. Gao, B. W. Liu; Almost periodic solution for a class of Lienard-type systems with multiple varying time delays, Applied Mathematical Modelling 34 (2010), 72-79.
• Xu, Changjin; Liao, Maoxin Existence and uniqueness of pseudo almost periodic solutions for Liénard-type systems with delays. Electron. J. Differential Equations 2016, Paper No. 170, 8 pp.
• Xu, Y., Positive almost periodic solutions for a class of nonlinear Duffing equations with a deviating argument. Electron. J. Qual. Theory Differ. Equ., 49 (2012), 1-9.
• Peng, L.Q., Wang, W.T, Positive almost periodic solutions for a class of nonlinear Duffing equations with a deviating argument. Electron. J. Qual. Theory Differ. Equ., 49 (2010), 1-12.
• Liu, B., Tunc, C., Pseudo almost periodic solutions for a class of nonlinear Duffing system with a deviating argument. J. Appl. Math. Comput., 49 (2015), 233-242.
• Diagana, T., Existence of weighted pseudo almost periodic solutions to some non-autonomous differential equations. Int. J. Evol. Equ.,2 (2008),397–410.
• Diagana, T.,Weighted pseudo-almost periodic solutions to some differential equations. Non-linear Anal. 8 (2008), 2250-2260.
• M’hamdi, M. S, Aouiti, C., Touati,A.; Alimi, Adel M.; Snasel., Weighted pseudo almost-periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Acta Math. Sci. Ser. B Engl. Ed., 36 (2016), 1662-1682.
• Zhao,L., Li, Y., Global exponential stability of weighted pseudo-almost periodic solutions of neutral type high-order Hopfield neural networks with distributed delays. Abstr. Appl. Anal., (2014), 17 pp.
• Xu, Y., Weighted pseudo-almost periodic delayed cellular neural networks. Neural Comput Appl, 28 (2017), 1-6.