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

1999
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Annales Polonici Mathematici
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The linear homogeneous differential equation with variable delayṡ is considered, where α j ∈ C(I, R + ), I = [t 0 , ∞), R + = (0, ∞), n j=1 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. 1991 Mathematics Subject

doi:10.4064/ap-72-2-115-130
fatcat:jrkqpxdznfbxhjdjejpbhge72u