Stability by decompositions for Volterra equations (Q1067159)
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scientific article; zbMATH DE number 3927625
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability by decompositions for Volterra equations |
scientific article; zbMATH DE number 3927625 |
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Stability by decompositions for Volterra equations (English)
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1985
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The stability of the zero solution of the integro-differential equation \(\dot x(\)t)\(=A(t)x(t)+\int^{t}_{0}C(t,s)x(s)ds\), \(x(t)\in {\mathbb{R}}^ n\), is studied. A number of Ljapunov functionals is constructed for a modified version of this equation yielding sufficient conditions for instability, stability and asymptotic stability. For certain classes of equations the above conditions are also necessary.
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Ljapunov functionals
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instability
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asymptotic stability
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