一类非线性中立型脉冲时滞微分方程解的渐近性

Abstract

Abstract:

This paper is concerned with the
nonlinear impulsive neutral delay differential equation with
positive and negative coefficients,
$$
\left\{
\begin{array}{ll}
[x(t)-c(t)x(t-\tau)]'+p(t)f(x(t-\delta))-q(t)f(x(t-\sigma))=0,\quad
t\geq t_0,~ t\not= t_k, \\
x(t_k)= b_kx(t_k^-)\\
\disp\qquad \quad\ \ +(1-b_k)\left(\int^{t_k}_{t_k-\delta}p(s+\delta)f(x(s)){\rm d}s-
\int^{t_k}_{t_k-\sigma}q(s+\sigma)f(x(s)){\rm d}s\right),\\
\hskip 9.7cm k=1,2,3,\cdots.
\end{array}
\right.
$$
Sufficient conditions are obtained for every solution of
the above equation tending to a constant as $t\to \infty$.

Key words: Asymptotic behavior, Liapunov functional, Neutral delay differential equation, Impulse

CLC Number:

34K20

WEI Geng-Ping, SHEN Jian-Hua. Asymptotic Behavior for a Class of Nonlinear Impulsive Neutral Delay Differential Equations[J].Acta mathematica scientia,Series A, 2010, 30(3): 753-763.

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References

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Asymptotic Behavior for a Class of Nonlinear Impulsive Neutral Delay Differential Equations

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