Displaying similar documents to “Convergence tests for one scalar differential equation with vanishing delay”

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

Josef Diblík (1999)

Annales Polonici Mathematici

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The linear homogeneous differential equation with variable delays ẏ ( t ) = ∑ j = 1 n α j ( t ) [ y ( t ) - y ( t - τ j ( t ) ) ] is considered, where α j ∈ C ( I , ℝ ͞ ͞ ⁺ ) , I = [t₀,∞), ℝ⁺ = (0,∞), ∑ j = 1 n α j ( t ) > 0 on I, τ j ∈ C ( I , ℝ ⁺ ) , the functions t - τ j ( t ) , j=1,...,n, are increasing and the delays τ 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.