Wong’s oscillation theorem for second-order delay differential equations
Let H(t) := ∫1/(r(s)z²(s)) (∫z(k)f(k)dk) ds, where z is a positive solution of (r(t)x')' + q(t)x = 0, t ≥ a, satisfying ∫1 / (r(s)z²(s)) ds < ∞. It is well known that, see [J. S. W. Wong, J. Math. Anal. and Appl. — 1999. — 231. — P. 235 – 240], if limt→∞ H(t) = − lim t→∞ H...
Збережено в:
| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/177242 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Wong’s oscillation theorem for second-order delay differential equations / A. Özbekler and A. Zafer // Нелінійні коливання. — 2016. — Т. 19, № 1. — С. 93-100 — Бібліогр.: 15 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Let
H(t) := ∫1/(r(s)z²(s)) (∫z(k)f(k)dk) ds,
where z is a positive solution of
(r(t)x')' + q(t)x = 0, t ≥ a,
satisfying
∫1 / (r(s)z²(s)) ds < ∞.
It is well known that, see [J. S. W. Wong, J. Math. Anal. and Appl. — 1999. — 231. — P. 235 – 240], if
limt→∞ H(t) = − lim t→∞ H(t) = ∞,
then every solution of
(r(t)x') + q(t)x = f(t)
is oscillatory.
In this paper we extend Wong’s result to delay differential equations of the form
(r(t)x' (t))' + q(t)x(τ(t)) = f(t).
It is observed that the oscillation behavior may be altered due to presence of the delay. Extensions to Emden – Fowler type delay differential equations are also discussed. |
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