### A criterion for convergence of solutions of homogeneous delay linear differential equations

The linear homogeneous differential equation with variable delays $\u1e8f\left(t\right)={\sum}_{j=1}^{n}{\alpha}_{j}\left(t\right)[y\left(t\right)-y(t-{\tau}_{j}\left(t\right))]$ is considered, where ${\alpha}_{j}\in C(I,\mathbb{R}\u035e\u035e\u207a)$, I = [t₀,∞), ℝ⁺ = (0,∞), ${\sum}_{j=1}^{n}{\alpha}_{j}\left(t\right)>0$ on I, ${\tau}_{j}\in C(I,\mathbb{R}\u207a),$ the functions $t-{\tau}_{j}\left(t\right)$, j=1,...,n, are increasing and the delays ${\tau}_{j}$ are bounded. A criterion and some sufficient conditions for convergence of all solutions of this equation are proved. The related problem of nonconvergence is also discussed. Some comparisons to known results are given.