A criterion for convergence of solutions of homogeneous delay linear differential equations
Tom 72 / 1999
Annales Polonici Mathematici 72 (1999), 115-130
DOI: 10.4064/ap-72-2-115-130
Streszczenie
The linear homogeneous differential equation with variable delays is considered, where α_j ∈ C(I,ℝ͞͞⁺), 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.