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

Annales Polonici Mathematici (1999)

- Volume: 72, Issue: 2, page 115-130
- ISSN: 0066-2216

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topDiblík, Josef. "A criterion for convergence of solutions of homogeneous delay linear differential equations." Annales Polonici Mathematici 72.2 (1999): 115-130. <http://eudml.org/doc/262578>.

@article{Diblík1999,

abstract = {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.},

author = {Diblík, Josef},

journal = {Annales Polonici Mathematici},

keywords = {topological principle of Ważewski (Rybakowski's approach); asymptotic convergence of solutions; linear homogeneous delay differential equation; topological principle of Rybakowski},

language = {eng},

number = {2},

pages = {115-130},

title = {A criterion for convergence of solutions of homogeneous delay linear differential equations},

url = {http://eudml.org/doc/262578},

volume = {72},

year = {1999},

}

TY - JOUR

AU - Diblík, Josef

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

JO - Annales Polonici Mathematici

PY - 1999

VL - 72

IS - 2

SP - 115

EP - 130

AB - 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.

LA - eng

KW - topological principle of Ważewski (Rybakowski's approach); asymptotic convergence of solutions; linear homogeneous delay differential equation; topological principle of Rybakowski

UR - http://eudml.org/doc/262578

ER -

## References

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