Existence of pseudo almost periodic solutions of linear Volterra integrodifferential equations (Q2919586)
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scientific article; zbMATH DE number 6090206
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of pseudo almost periodic solutions of linear Volterra integrodifferential equations |
scientific article; zbMATH DE number 6090206 |
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4 October 2012
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linear Volterra equations
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pseudo almost periodic solutions
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exponential asymptotical stability
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Existence of pseudo almost periodic solutions of linear Volterra integrodifferential equations (English)
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The paper is concerned with the linear equation NEWLINE\[NEWLINEx'(t)=A(t)x(t)+{\int}_{-\infty}^t F(t,s) x(s)\, ds+p(t),\quad t\in\mathbb R.NEWLINE\]NEWLINE In order to obtain existenceof solutions for this equation, the authors give some characterizations for the exponential asymptotic stability of the zero solution of the homogeneous equation (i.e., the equation corresponding to \(p\equiv 0\)). An example is also discussed in the last section.
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