Periodic boundary value problems for integro-differential equations in Banach spaces (Q1777560)
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scientific article; zbMATH DE number 2170647
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodic boundary value problems for integro-differential equations in Banach spaces |
scientific article; zbMATH DE number 2170647 |
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Periodic boundary value problems for integro-differential equations in Banach spaces (English)
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23 May 2005
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Periodic solutions of the integro-differential equation \[ u'(t)=H\biggl(t,u(t),\int_0^th(t,s)u(s)\,ds\biggr) \] is studied in an ordered Banach space. It is assumed that certain upper and lower solutions exist and that \(H\) satisfies some monotonicity type conditions. Under these hypotheses, the existence of maximal and minimal solutions is obtained.
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integro-differential equation
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ordered Banach space
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maximal and minimal solution
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upper and lower solution
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periodic solutions
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