On a general nonlinear problem with distributed delays. (English) Zbl 1375.34109
J. Contemp. Math. Anal., Armen. Acad. Sci. 52, No. 4, 184-190 (2017) and Izv. Nats. Akad. Nauk Armen., Mat. 52, No. 4, 72-80 (2017).
From the introduction: We deal with the following system of equations:
\[
x_i'(t)=- a_i(t) x_i(t)+ \sum^m_{j=1} f_{ij}\Biggl(t, x_j(t),\;\int^t_{-\infty} K_{ij}(t,s,x_j(s))\,ds\Biggr)+ c_i(t),
\]
\(i= 1,\dots, m\), with given continuous functions \(x_j(t)= x_{0j}(t)\), \(t\in(-\infty, 0]\), \(a_i(t)\geq 0\) and \(c_i(t)\), \(i= 1,\dots, m\), \(t>0\). The functions \(f_{ij}\) and \(K_{ij}\), \(i,j= 1,\dots, m\), are assumed to be nonlinear and continuous, and satisfy some conditions.
MSC:
| 34K25 | Asymptotic theory of functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
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