The freezing method for Volterra integral equations in a Banach space
The "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type $$ x(t)- \int_0^t K(t, t-s)x(s)ds =f(t)\;(t\geq 0),$$ where $K(t,s)$ is an operator valued function "slowly" varying in the first argument. Bes...
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| Format: | Article |
| Language: | English |
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University of Szeged
2008-04-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=307 |
| Summary: | The "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type $$ x(t)- \int_0^t K(t, t-s)x(s)ds =f(t)\;(t\geq 0),$$ where $K(t,s)$ is an operator valued function "slowly" varying in the first argument. Besides, sharp explicit stability conditions are derived. |
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| ISSN: | 1417-3875 1417-3875 |