Global existence and boundedness of a certain nonlinear vector integro differential equation of second order with multiple deviating arguments. (English) Zbl 1390.45013
The following vector integro-differential equation with multiple deviating arguments is considered
\[
(r(t)X^{\prime})^{\prime} + A(t)F(X,X^{\prime})X^{\prime} + B(t)E(X^{\prime}) + \sum\limits_{i=1}^{n}G_i(t)H_i(X(t-\tau_i)) = \int\limits_0^t K(t,s)X^{\prime}(s)ds.
\]
Based on the Lyapunov-Krasovskii functional approach, the global existence and boundedness of all solutions of this equation are discussed. An example illustrates the theoretical analysis made in this study and shows the effectiveness of the method used here.
Reviewer: Temur A. Jangveladze (Tbilisi)
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