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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |