Using Banach Fixed Point Theorem To Study The Stability Of First-Order Delay Differential Equations

  • Zaid A. A. Mahdi Monje Department of Mathematics, College of Science, University of Baghdad
  • Buthainah A. A. Ahmed Department of Mathematics, College of Science, University of Baghdad
Keywords: Banach Fixed Point Theorem, First-Order Delay, stability, Differential Equations

Abstract

In1 this1 paper1 we1 use the Banach fixed point theorem investigate 1the stability and asymptotic1 stability1 of the zero solution for the first order retarded delay differential equation 

1(y(t)) ́=-∑_(j=1)^N▒〖b_j (t ,〖3y〗_t )3y(t)+f(t ,〖3y〗_t)〗

where the delay is constant. Also we give new conditions to ensure the stability and asymptotic stability of the zero solution of this equation.

References

[1] Burton, T. A.; Furumochi, T.; “Fixed points and problems in stability theory for ordinary and functional differential equations”; Proc. Dynamic Syst. Appl. 10, 89-116, 2001.
[2] Burton, T. A.; Furumochi, T.; “Asymptotic behavior of solutions of functional differential equations by fixed point theorems”; Proc. Dynamic Syst. Appl. 11, 499-519, 2002.
[3] Burton, T. A.; “Stability by Fixed Point Theory for Functional Differential Equations”; Dover Publ. Inc.; 2006.
[4] Erwin, K.; “Introductory Functional Analysis with Applications, University of Windsor”; 1989.
[5] Border, K. C.; “Differentiating an Integral: Leibniz' Rule”; Caltech Division of the Humanities and Social Sciences; 2016.
[6] Meng, F.; Zhinan, X.; Huaiping, Z.; “Asymptotic stability of delay differential equations via fixed point theory and applications”; Canadian Appl. Math. Quart. 2010.
[7] Bo, Z.; “Fixed points and Stability in differential equations with variable delays, Department of Mathematics and Computer Science, Fayetteville State University”; Fayetteville, NC 28301, USA; 2005.
[8] Ramazan, Y.; Cemil, T.; Ӧzkan, A.; “On the Global Asymptotic Stability of Solution to neutral equations of first order”; Palestine J. Mathematics, 2017.
Published
2020-03-04
How to Cite
Zaid A. A. Mahdi Monje, & Buthainah A. A. Ahmed. (2020). Using Banach Fixed Point Theorem To Study The Stability Of First-Order Delay Differential Equations. Al-Nahrain Journal of Science, 23(1), 69-72. Retrieved from http://anjs.edu.iq/index.php/anjs/article/view/2243
Section
Articles