### On a boundary value problem for a two-dimensional system of evolution functional differential equations.

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Sufficient conditions are established for the oscillation of proper solutions of the system $$\begin{array}{cc}\hfill {u}_{1}^{\text{'}}\left(t\right)& =p\left(t\right){u}_{2}\left(\sigma \left(t\right)\right)\phantom{\rule{0.166667em}{0ex}},\hfill \\ \hfill {u}_{2}^{\text{'}}\left(t\right)& =-q\left(t\right){u}_{1}\left(\tau \left(t\right)\right)\phantom{\rule{0.166667em}{0ex}},\hfill \end{array}$$ where $p,\phantom{\rule{0.166667em}{0ex}}q:{R}_{+}\to {R}_{+}$ are locally summable functions, while $\tau $ and $\sigma :{R}_{+}\to {R}_{+}$ are continuous and continuously differentiable functions, respectively, and $\underset{t\to +\infty}{lim}\tau \left(t\right)=+\infty $, $\underset{t\to +\infty}{lim}\sigma \left(t\right)=+\infty $.

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