- Research Article
- Open Access
Exponential stability in a scalar functional differential equation
Journal of Inequalities and Applications volume 2006, Article number: 37195 (2006)
We establish a criterion for the global exponential stability of the zero solution of the scalar retarded functional differential equation whose linear part generates a monotone semiflow on the phase space with respect to the exponential ordering, and the nonlinearity has at most linear growth.
Azbelev NV, Simonov PM: Stability of Differential Equations with Aftereffect, Stability and Control: Theory, Methods and Applications. Volume 20. Taylor & Francis, London; 2003:xviii+222.
Berezansky L, Braverman E: On exponential stability of linear differential equations with several delays. Journal of Mathematical Analysis and Applications 2006,324(2):1336–1355. 10.1016/j.jmaa.2006.01.022
Berezansky L, Braverman E: On stability of some linear and nonlinear delay differential equations. Journal of Mathematical Analysis and Applications 2006,314(2):391–411. 10.1016/j.jmaa.2005.03.103
Faria T, Huang W: Special solutions for linear functional differential equations and asymptotic behaviour. Differential and Integral Equations 2005,18(3):337–360.
Gusarenko SA, Domoshnitskiĭ AI: Asymptotic and oscillation properties of first-order linear scalar functional-differential equations. Differential Equations 1989,25(12):1480–1491 (1990).
Győri I: Interaction between oscillations and global asymptotic stability in delay differential equations. Differential and Integral Equations 1990,3(1):181–200.
Hale J: Theory of Functional Differential Equations. Springer, New York; 1977:x+365.
Pituk M: Convergence to equilibria in scalar nonquasimonotone functional differential equations. Journal of Differential Equations 2003,193(1):95–130. 10.1016/S0022-0396(03)00147-5
Smith HL: Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs. Volume 41. American Mathematical Society, Rhode Island; 1995:x+174.
Smith HL, Thieme HR: Monotone semiflows in scalar non-quasi-monotone functional-differential equations. Journal of Mathematical Analysis and Applications 1990,150(2):289–306. 10.1016/0022-247X(90)90105-O
About this article
Cite this article
Liz, E., Pituk, M. Exponential stability in a scalar functional differential equation. J Inequal Appl 2006, 37195 (2006). https://doi.org/10.1155/JIA/2006/37195
- Differential Equation
- Phase Space
- Linear Part
- Linear Growth
- Exponential Stability