The freezing method for volterra integral equations in a Banach space

M. I. Gil

doi:10.14232/ejqtde.2008.1.17

The freezing method for volterra integral equations in a Banach space

M. I. Gil

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type x(t) - ∫₀^t K(t, t - s)x(s)ds = f(t) (t ≥ 0), where K(t,s) is an operator valued function "slowly" varying in the first argument. Besides, sharp explicit stability conditions are derived.

Original language	English
Pages (from-to)	1-7
Number of pages	7
Journal	Electronic Journal of Qualitative Theory of Differential Equations
DOIs	https://doi.org/10.14232/ejqtde.2008.1.17
State	Published - 1 Jan 2008

Keywords

Banach space
Stability
Volterra integral equations

ASJC Scopus subject areas

Applied Mathematics

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10.14232/ejqtde.2008.1.17

Cite this

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N2 - The "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type x(t) - ∫0t K(t, t - s)x(s)ds = f(t) (t ≥ 0), where K(t,s) is an operator valued function "slowly" varying in the first argument. Besides, sharp explicit stability conditions are derived.

AB - The "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type x(t) - ∫0t K(t, t - s)x(s)ds = f(t) (t ≥ 0), where K(t,s) is an operator valued function "slowly" varying in the first argument. Besides, sharp explicit stability conditions are derived.

KW - Banach space

KW - Stability

KW - Volterra integral equations

UR - https://www.scopus.com/pages/publications/42949120542

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DO - 10.14232/ejqtde.2008.1.17

M3 - Article

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JO - Electronic Journal of Qualitative Theory of Differential Equations

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ER -

The freezing method for volterra integral equations in a Banach space

Abstract

Keywords

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