Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument
The characteristic equation for an equation with continuous and piecewise constant argument in the form x˙(t)+px(t−τ)+qx([t−k])=0 where p, q∈ℜ, τ∈ℜ+and k∈ℵ is presented, which when q=0 reduces to f(λ)=λ+e−λτ=0 and when p=0 reduces to λ−1+qλ−k=0. Also, the necessary and sufficient conditions f...
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Hindawi Limited
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171298000702 |
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doaj-a3e8b377eaac4b4c858c60640844dbbf2020-11-24T22:09:56ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121349349710.1155/S0161171298000702Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argumentH. A. Agwo0Department of Mathematics, Faculty of Education, Ain Shams University, Roxy , Cairo, EgyptThe characteristic equation for an equation with continuous and piecewise constant argument in the form x˙(t)+px(t−τ)+qx([t−k])=0 where p, q∈ℜ, τ∈ℜ+and k∈ℵ is presented, which when q=0 reduces to f(λ)=λ+e−λτ=0 and when p=0 reduces to λ−1+qλ−k=0. Also, the necessary and sufficient conditions for oscillation are obtained.http://dx.doi.org/10.1155/S0161171298000702OscillationsDelay differential equations. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
H. A. Agwo |
| spellingShingle |
H. A. Agwo Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument International Journal of Mathematics and Mathematical Sciences Oscillations Delay differential equations. |
| author_facet |
H. A. Agwo |
| author_sort |
H. A. Agwo |
| title |
Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument |
| title_short |
Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument |
| title_full |
Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument |
| title_fullStr |
Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument |
| title_full_unstemmed |
Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument |
| title_sort |
necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1998-01-01 |
| description |
The characteristic equation for an equation with continuous and piecewise constant
argument in the form
x˙(t)+px(t−τ)+qx([t−k])=0 where p, q∈ℜ, τ∈ℜ+and k∈ℵ is presented, which when
q=0 reduces to
f(λ)=λ+e−λτ=0
and when p=0 reduces to
λ−1+qλ−k=0.
Also, the necessary and sufficient conditions for oscillation are obtained. |
| topic |
Oscillations Delay differential equations. |
| url |
http://dx.doi.org/10.1155/S0161171298000702 |
| work_keys_str_mv |
AT haagwo necessaryandsufficientconditionsfortheoscillationofdelaydifferentialequationwithapiecewiseconstantargument |
| _version_ |
1725809864560607232 |