Asymptotic behavior of solutions for nonlinear delay differential equation with impulses

作者：Shen, Jianhua^*; Liu, Yanjun

来源：Applied Mathematics and Computation, 2009, 213(2): 449-454.

DOI：10.1016/j.amc.2009.03.043

• Asymptotic behavior
• Liapunov functional
• Differential equation
• Impulse

This paper studies the asymptotic behavior of solutions of the nonlinear delay differential equation with impulses
{x'(t) + p(t)f(x(t - tau)) = 0 t >= t(0), t not equal t(k),
x(t(k)) = b(k)x(t(k)(-)) + (1-b(k)) integral(tk)(tk-tau)p(s+tau)f(x(s))ds k is an element of Z(+).
Sufficient conditions are obtained under which every solution of the equation tends to a constant or zero as t -> infinity. Our results improve and generalize some known ones.

• 出版日期2009-7-15
• 单位长沙学院; 杭州师范大学