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Asymptotic behavior of solutions of nonlinear neutral differential equations with impulses. (English) Zbl 1118.34073

Summary: This paper is concerned with a nonlinear neutral differential equations with impulses of the form \[ [x(t)+C(t)x(t-\tau)]'+P(t)f(x(t-\delta))=0,\quad t\geq t_0,\;t\neq t_k,\tag{*} \]
\[ x(t_k)=b_kx(t_k^-)+(1-b_k) \int^{t_k}_{t_k-\delta}P(s+\delta) f(x(s))\,ds,\quad k=1,2,\dots.\tag{**} \] Sufficient conditions are obtained for every solution of (*) and (**) that tends to a constant as \(t\to\infty\).

MSC:

34K25 Asymptotic theory of functional-differential equations
34K45 Functional-differential equations with impulses
34K40 Neutral functional-differential equations
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