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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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000702 |
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| _version_ | 1832553000402419712 |
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| author | H. A. Agwo |
| author_facet | H. A. Agwo |
| author_sort | H. A. Agwo |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-a3e8b377eaac4b4c858c60640844dbbf |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a3e8b377eaac4b4c858c60640844dbbf2025-02-03T05:57:10ZengWileyInternational 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. |
| 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. |
| title | 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_short | 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 |
| topic | Oscillations Delay differential equations. |
| url | http://dx.doi.org/10.1155/S0161171298000702 |
| work_keys_str_mv | AT haagwo necessaryandsufficientconditionsfortheoscillationofdelaydifferentialequationwithapiecewiseconstantargument |