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A comparison theorem for linear delay differential equations

Jozef Džurina (1995)

Archivum Mathematicum

In this paper property (A) of the linear delay differential equation L n u ( t ) + p ( t ) u ( τ ( t ) ) = 0 , is to deduce from the oscillation of a set of the first order delay differential equations.

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

Josef Diblík (1999)

Annales Polonici Mathematici

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

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