Asymptotic stability of the zero solution for degenerate retarded differential equations

作者：Zhou Xian Feng; Liang Jin; Xiao Ti Jun

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 70(3): 1415-1421.

DOI：10.1016/j.na.2008.02.022

• Functional differential equation
• Characteristic root
• Asymptotic stability
• Retarded

In this paper, we mainly discuss relations between the asymptotic stability of the zero solution for retarded differential equations and real parts of all characteristic roots of characteristic equations, We obtain a necessary and Sufficient condition for the asymptotic stability of the zero solution. We point out the mistake of [W.E. Brumley, On the asymptotic behavior Of Solutions of differential-difference equations of neutral type, Journal of Differential Equations 7 (1) (1970) 175-188], generalize the result of [H. Ren, Z. Zhen, Algebraic criteria of asymptotic stability of zero solution of neutral-type equation (x) over dot(t) c(x) over dot(t - tau) ax(t) bx(t - tau) = 0, Acta Mathematica Sinica 42 (6) (1999) 1-11] and solve a problem posed in [Z-X. Zheng, Introduction to Functional Differential Equations, Anhui Educational Press, 1992].

• 出版日期2009-2-1
• 单位中国科学技术大学; 安徽大学