Asymptotic formulas for a scalar linear delay differential equation
The linear delay differential equation x 0 (t) = p(t)x(t − r) is considered, where r > 0 and the coefficient p : [t0, ∞) → R is a continuous function such that p(t) → 0 as t → ∞. In a recent paper [M. Pituk, G. Röst, Bound. Value Probl. 2014:114] an asymptotic description of the solutions has bee...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2016
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| Sorozat: | Electronic journal of qualitative theory of differential equations : special edition
2 No. 72 |
| Kulcsszavak: | Differenciálegyenlet - késleltetett |
| doi: | 10.14232/ejqtde.2016.1.72 |
| Online Access: | http://acta.bibl.u-szeged.hu/73739 |
| Tartalmi kivonat: | The linear delay differential equation x 0 (t) = p(t)x(t − r) is considered, where r > 0 and the coefficient p : [t0, ∞) → R is a continuous function such that p(t) → 0 as t → ∞. In a recent paper [M. Pituk, G. Röst, Bound. Value Probl. 2014:114] an asymptotic description of the solutions has been given in terms of a special solution of the associated formal adjoint equation and the initial data. In this paper, we give a representation of the special solution of the formal adjoint equation. Under some additional conditions, the representation theorem yields explicit asymptotic formulas for the solutions as t → ∞. |
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| Terjedelem/Fizikai jellemzők: | 14 |
| ISSN: | 1417-3875 |