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

100%

Diblík J.

Annales Polonici Mathematici

1999

tom 72

nr 2

115-130

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 $α_j ∈ C(I,ℝ͞͞⁺)$, 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.

Asymptotic behaviour of solutions of linear differential equations with delay

100%

Diblík J.

Annales Polonici Mathematici

1993

tom 58

nr 2

131-137

Inequalities for some positive solutions of the linear differential equation with delay ẋ(t) = -c(t)x(t-τ) are obtained. A connection with an auxiliary functional nondifferential equation is used.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Diblík J.

1 1999

1 1993

Wyniki wyszukiwania

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

Asymptotic behaviour of solutions of linear differential equations with delay